Resistance

What Is Electrical Resistance?

Electrical resistance describes how strongly a material or component opposes the flow of electric current.

When a potential difference is applied across a conductor, an electric field causes charge carriers to move. In a metal, these charge carriers are mainly free electrons.

As the electrons move through the material, they interact with the atoms and ions in the material. These interactions make it more difficult for charge to flow.

Resistance is represented by:

R

and its SI unit is the:

ohm (Ω)

A component with a high resistance allows less current to flow for a given voltage than a component with a low resistance.

 

 

 

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Resistance, Voltage and Current

Resistance is closely related to potential difference (voltage) and current.

For an ohmic conductor:

R = V/I

where:

• R = resistance in ohms (Ω)
• V = potential difference in volts (V)
• I = current in amperes (A)

This can also be rearranged:

V = IR

and:

I = V/R

These relationships form Ohm's Law.

Understanding R = V/I

Resistance tells us how much voltage is required to produce a particular current.

Suppose:

V = 12 V

I = 3 A

Then:

R = V/I

R = 12/3

R = 4 Ω

The component has a resistance of 4 Ω.

Comparing Different Resistances

Suppose two resistors are connected separately to the same 12 V supply.

Resistor A:

R = 3 Ω

I = V/R

I = 12/3

I = 4 A

Resistor B:

R = 6 Ω

I = 12/6

I = 2 A

The higher-resistance component allows less current to flow.

For the same voltage:

higher resistance → lower current

lower resistance → higher current

What Causes Resistance?

In a metal, some electrons are free to move throughout the material.

Without an applied electric field, these electrons move randomly.

When a voltage is applied, the electric field causes the electrons to develop an overall drift through the conductor.

However, the electrons do not travel freely from one end of the wire to the other.

They continually interact with the metal's lattice of positive ions.

These interactions oppose the organized movement of charge and produce electrical resistance.

 

 

 

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Microscopic View of Resistance

A useful microscopic model is:

electric field → electron drift → interactions with lattice → resistance

The electrons gain energy from the electric field between interactions.

When they interact with the lattice, some of this energy is transferred to the material.

This increases the internal energy of the conductor.

As a result, the conductor may become warmer.

This is why resistors and wires can heat up when current flows through them.

Resistance and Energy Transfer

Electrical resistance does not mean that electrons are simply "used up."

Instead, energy is transferred.

Electrical energy can be converted into thermal energy as charges move through a resistive material.

The power transferred can be calculated using:

P = VI

Using V = IR gives:

P = I²R

Another useful form is:

P = V²/R

These equations help explain electrical heating.

Resistance in Heating Devices

Resistance is deliberately used in many devices to produce thermal energy.

Examples include:

• electric kettles
• toasters
• electric ovens
• hair dryers
• space heaters
• electric blankets

A heating element is designed to have enough resistance to convert electrical energy into thermal energy effectively.

 

 

 

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Factors Affecting Resistance

The resistance of a wire depends mainly on:

• its length
• its cross-sectional area
• the material
• its temperature

For a uniform conductor:

R = ρL/A

where:

• R = resistance (Ω)
• ρ = resistivity (Ω·m)
• L = length (m)
• A = cross-sectional area (m²)

This equation allows us to separate the effects of the material from the dimensions of the conductor.

Effect of Length

Resistance increases with the length of a wire.

For the same material and cross-sectional area:

R ∝ L

A longer wire provides a longer path through which electrons must travel.

This means more opportunities for interactions with the lattice.

Therefore:

longer wire → greater resistance

If the length doubles while everything else remains constant:

resistance doubles

Example: Changing Length

A wire has:

R = 5 Ω

If its length is doubled while its material, temperature and cross-sectional area remain unchanged:

R_new = 10 Ω

If its length is tripled:

R_new = 15 Ω

Resistance is directly proportional to length.

 

 

 

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Effect of Cross-Sectional Area

Resistance decreases as the cross-sectional area increases.

R ∝ 1/A

A thicker wire provides more space for charge to flow.

Therefore:

larger area → lower resistance

smaller area → higher resistance

If the cross-sectional area doubles:

resistance halves

provided all other factors remain constant.

Why Thick Wires Have Lower Resistance

Imagine charge moving through two wires made of the same material.

A thin wire provides a relatively narrow pathway.

A thick wire provides many more possible pathways for charge carriers.

This reduces the resistance.

This is why electrical cables designed to carry large currents generally use relatively thick conductors.

 

 

 

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Diameter and Cross-Sectional Area

For a circular wire:

A = πr²

where r is the radius.

Because area depends on the square of the radius, changing the diameter can have a large effect on resistance.

Suppose the radius doubles.

Then:

A_new = π(2r)²

A_new = 4πr²

The area becomes four times larger.

Since:

R ∝ 1/A

the resistance becomes:

one-quarter of its original value

This is an important distinction: doubling the radius does not simply halve the resistance.

Worked Example Using R = ρL/A

A wire has:

ρ = 1.7 × 10⁻⁸ Ω·m

L = 5.0 m

A = 1.0 × 10⁻⁶ m²

Calculate its resistance.

Use:

R = ρL/A

R = (1.7 × 10⁻⁸)(5.0)/(1.0 × 10⁻⁶)

R = 8.5 × 10⁻² Ω

Therefore:

R = 0.085 Ω

What Is Resistivity?

Resistivity is a property of a material that describes how strongly the material resists electric current.

It is represented by:

ρ

Its SI unit is:

Ω·m

Resistance and resistivity are related, but they are not the same thing.

Resistance depends on both the material and the object's dimensions.

Resistivity is a property of the material itself at a given temperature.

Resistance vs Resistivity

For example, two copper wires can have different resistances because they have different lengths or thicknesses.

However, at the same temperature, the copper in both wires has approximately the same resistivity.

Comparing Materials

Different materials have very different resistivities.

Materials with low resistivity are good electrical conductors.

Examples include:

• silver
• copper
• gold
• aluminium

Materials with high resistivity resist charge flow much more strongly.

Examples include:

• rubber
• glass
• plastics
• ceramics

This difference is why copper can be used for the conducting core of a cable while plastic is used around it as insulation.

 

 

 

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Conductors

A conductor is a material through which electric charge can move relatively easily.

Metals are good conductors because they contain many mobile electrons.

Copper is widely used in electrical wiring because it combines:

• low resistivity
• good mechanical properties
• relatively reasonable cost
• good durability

Silver has even lower resistivity but is much more expensive.

Insulators

An insulator has very few mobile charge carriers under normal conditions.

Examples include:

• rubber
• plastic
• glass
• dry wood
• ceramic

Insulators are important for electrical safety because they prevent unwanted current from flowing.

Electrical cables therefore commonly combine:

conducting metal core + insulating outer layer

What Is a Resistor?

A resistor is an electrical component designed to provide a particular amount of resistance.

Resistors can be used to:

• limit current
• divide voltage
• protect components
• control circuit behavior
• produce heating
• establish operating conditions in electronic circuits

A conductor is a material, while a resistor is a component designed to have useful electrical resistance.

 

 

 

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Conductors Still Have Resistance

Calling something a conductor does not mean its resistance is zero.

Copper wire has a low resistivity, but a long, thin copper wire can still have significant resistance.

The equation:

R = ρL/A

shows why.

Even if ρ is small:

• increasing L increases R
• decreasing A increases R

Real conductors normally have some resistance.

Effect of Temperature on Metals

For most metals:

temperature increases → resistance increases

As a metal becomes hotter, its lattice ions vibrate more strongly.

The moving electrons then experience more frequent or stronger interactions with the lattice.

This makes organized electron flow more difficult.

Therefore:

higher temperature → greater resistance

for ordinary metallic conductors.

Microscopic Explanation of Temperature Effects

At lower temperature, lattice ions vibrate less.

Electrons can move through the material with fewer disruptions.

At higher temperature, lattice vibrations become larger.

The moving electrons are scattered more frequently.

Therefore, resistance increases.

This microscopic model connects:

temperature → lattice vibration → electron scattering → resistance

 

 

 

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Resistance and Temperature Equation

Over a limited temperature range, the resistance of many metals can be approximated by:

R = R₀[1 + α(T − T₀)]

where:

• R = resistance at temperature T
• R₀ = resistance at reference temperature T₀
• α = temperature coefficient of resistance
• T − T₀ = temperature change

This relationship is approximately linear over suitable temperature ranges.

Temperature Sensors

The relationship between resistance and temperature can be useful.

A resistance temperature detector (RTD) measures temperature by measuring changes in electrical resistance.

Some other sensors, called thermistors, also change resistance strongly with temperature.

These devices are used in:

• thermostats
• digital thermometers
• appliances
• vehicles
• laboratory equipment
• electronic systems

Ohmic Conductors

An ohmic conductor obeys Ohm's Law when its physical conditions, especially temperature, remain constant.

For an ohmic conductor:

V ∝ I

and:

V/I = constant

Therefore:

R = constant

A fixed resistor may behave approximately this way over an appropriate operating range.

Non-Ohmic Components

Not every electrical component has constant resistance.

Examples include:

• filament lamps
• thermistors
• light-dependent resistors
• diodes

A filament lamp becomes extremely hot when current flows.

As its temperature rises, its resistance increases.

Therefore, voltage and current are not directly proportional across its entire operating range.

 

 

 

Resistance in a Filament Lamp

A lamp filament is usually made from a material such as tungsten.

When the lamp is switched on:

• current flows
• electrical energy is transferred
• the filament heats up
• lattice vibrations increase
• resistance increases

The filament becomes hot enough to emit visible light.

This provides a real-world example of the microscopic explanation of resistance.

Resistance and Electrical Safety

Resistance plays an important role in electrical safety.

Electrical wires carrying large currents can heat up because of:

P = I²R

Even a relatively small resistance can produce significant heating if the current is large.

For example, if:

I = 10 A

R = 0.5 Ω

then:

P = I²R

P = 10² × 0.5

P = 50 W

This energy transfer can heat the wire significantly.

This is one reason correct wire thickness is important.

Transmission of Electrical Energy

Resistance also matters when electrical energy is transmitted over long distances.

Power lost as thermal energy in transmission wires is approximately:

P_loss = I²R

Reducing the current greatly reduces these losses.

This is one reason electrical power is transmitted at very high voltages: for a given transmitted power, increasing voltage allows the current to be reduced.

Lower current means less energy is wasted heating the transmission wires.

 

 

 

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Superconductors

Some materials behave very differently at extremely low temperatures.

Below a particular critical temperature, certain materials become superconductors.

Their electrical resistance falls to essentially zero.

This allows current to flow with extremely small resistive energy losses.

Superconductors have applications in areas such as:

• powerful electromagnets
• MRI systems
• particle accelerators
• magnetic levitation
• scientific research

Superconductivity cannot be explained simply by the ordinary classical collision model used for normal metallic resistance.

Comparing a Conductor and a Resistor

Suppose we have a short copper wire and a 100 Ω resistor.

The copper wire is designed mainly to carry current with minimal resistance.

The resistor is designed to provide a controlled resistance.

Both conduct electricity, but they serve different purposes.

The distinction is therefore not:

conductor = no resistance

and:

resistor = resistance

Instead:

conductors are chosen to carry charge efficiently

while:

resistors are designed to provide a specific resistance

Worked Example: Comparing Wires

Wire A and Wire B are made from the same material and have the same cross-sectional area.

Wire B is three times as long as Wire A.

Since:

R ∝ L

Wire B has:

three times the resistance

of Wire A.

Worked Example: Changing Area

A wire has resistance:

R = 12 Ω

Its cross-sectional area is doubled while its length, material and temperature remain unchanged.

Since:

R ∝ 1/A

the new resistance is:

R_new = 12/2

R_new = 6 Ω

Worked Example: Length and Area Change Together

A wire has resistance:

R

A second wire of the same material has:

• twice the length
• twice the cross-sectional area

Using:

R = ρL/A

the length change would multiply resistance by 2.

The area change would divide resistance by 2.

Therefore:

R_new = R

The two effects cancel.

Common Mistakes

Mistake: Thinking resistance is the same as resistivity.
Resistance depends on the dimensions of an object. Resistivity is primarily a material property at a given temperature.

Mistake: Thinking good conductors have zero resistance.
Ordinary conductors still have resistance.

Mistake: Saying thicker wires have greater resistance.
For the same material and length, thicker wires have lower resistance.

Mistake: Saying longer wires have lower resistance.
Longer wires have greater resistance.

Mistake: Thinking current gets "used up" by resistance.
Charge is conserved. Resistance is associated with opposition to charge flow and energy transfer.

Mistake: Assuming all components have constant resistance.
Some components are non-ohmic, and resistance may change with temperature, light or other conditions.

Mistake: Saying electrons simply crash into stationary atoms.
A more accurate model describes electrons being scattered by the material's lattice, impurities, defects and lattice vibrations.

Key Terms

Electrical resistance — measure of how strongly a material or component opposes electric current.

Ohm (Ω) — SI unit of electrical resistance.

Ohm's Law — relationship V = IR for an ohmic conductor under constant physical conditions.

Resistivity (ρ) — material property describing opposition to electrical conduction.

Conductor — material containing mobile charge carriers that allow charge to move relatively easily.

Insulator — material in which charge carriers cannot move easily under ordinary conditions.

Resistor — component designed to provide a particular resistance.

Charge carrier — mobile charged particle responsible for electric current.

Drift — overall directed motion of charge carriers caused by an electric field.

Lattice — ordered arrangement of particles in a solid.

Scattering — interaction that changes the motion of charge carriers and contributes to resistance.

Cross-sectional area — area of a slice perpendicular to the length of a conductor.

Ohmic conductor — conductor for which V is proportional to I under constant physical conditions.

Temperature coefficient — measure of how strongly resistance changes with temperature.

Superconductor — material that can exhibit essentially zero electrical resistance below a critical temperature.

Key Takeaways

• Electrical resistance measures opposition to the flow of electric current.
• Resistance is measured in ohms (Ω).
• For an ohmic conductor, R = V/I.
• Higher resistance produces less current for the same voltage.
• The resistance of a uniform wire can be calculated using R = ρL/A.
• Longer wires have greater resistance.
• Thicker wires have lower resistance.
• Resistivity describes the electrical properties of the material itself.
• Low-resistivity materials such as copper are good conductors.
• Resistance and resistivity are related but are not the same quantity.
• Metals conduct because they contain mobile electrons.
• Electrical resistance can be understood microscopically through the scattering of moving electrons within the material.
• For most metals, increasing temperature increases resistance because lattice vibrations increase.
• Resistive components transfer electrical energy into thermal energy.
• Resistors deliberately provide resistance for controlling current and voltage in circuits.
• Conductors are normally selected to carry current with as little unwanted resistance as practical.
• Ordinary conductors do not have zero resistance.
• Electrical heating can be calculated using P = I²R.
• Resistance is important in circuit design, electrical heating, transmission systems and electrical safety.

Check Your Understanding

1. Define electrical resistance.
2. State the SI unit of resistance.
3. A resistor has 12 V across it and carries 3 A. Calculate its resistance.
4. A 20 Ω resistor is connected across 10 V. Calculate the current.
5. State four factors that can affect the resistance of a wire.
6. Explain why increasing the length of a wire increases its resistance.
7. Explain why increasing the cross-sectional area decreases resistance.
8. A wire's length doubles while everything else remains constant. What happens to its resistance?
9. A wire's cross-sectional area triples. What happens to its resistance?
10. Explain the difference between resistance and resistivity.
11. State the equation relating resistance, resistivity, length and cross-sectional area.
12. Explain why copper is commonly used for electrical wiring.
13. Explain microscopically why metals have electrical resistance.
14. Explain why the resistance of most metals increases when temperature increases.
15. Compare the purpose of a copper connecting wire with the purpose of a resistor.
16. Explain why a filament lamp does not maintain constant resistance while operating.
17. A wire is doubled in both length and cross-sectional area. Predict the change in resistance.
18. Explain why thick cables are used when large electrical currents must be carried.
19. Explain why electrical resistance can cause a wire to become warm.
20. Explain why reducing current reduces energy losses in electrical transmission wires.

Measuring Electrical Quantities

Measuring Current and Voltage

Electrical circuits can be investigated by measuring quantities such as:

• current
• potential difference (voltage)
• resistance

Two of the most important measuring instruments are the:

• ammeter — measures current
• voltmeter — measures potential difference

Modern laboratories often use a digital multimeter, which can perform both functions as well as measure resistance.

 

 

 

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Correctly connecting and reading these instruments is essential for obtaining reliable experimental data and avoiding damage to equipment.

Measuring Current

Electric current is the rate at which electric charge flows.

Current is represented by:

I

and measured in:

amperes (A)

The relationship is:

I = Q/t

where:

• I = current (A)
• Q = charge (C)
• t = time (s)

An ammeter is used to measure current.

Connecting an Ammeter

An ammeter must normally be connected in series with the component whose current is being measured.

This means the current being investigated must actually pass through the ammeter.

For example:

battery → ammeter → resistor → battery

The ammeter becomes part of the current path.

 

 

 

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Why Is an Ammeter Connected in Series?

An ammeter measures how much charge passes through it each second.

Therefore, the circuit current must flow through the meter.

An ideal ammeter has:

very low resistance

so that inserting it into the circuit changes the current as little as possible.

A real ammeter has a small resistance, but it is designed to be very low.

Never Connect an Ammeter Directly Across a Power Supply

An ammeter should not normally be connected directly across a battery or power supply.

Because an ammeter has very low resistance, this could create a very large current.

Possible consequences include:

• blown meter fuse
• damaged meter
• overheated wires
• damaged power supply
• unsafe heating

Always check the circuit before switching on the power.

Measuring Voltage

Potential difference, commonly called voltage, measures the energy transferred per unit charge between two points.

Voltage is represented by:

V

and measured in:

volts (V)

A voltmeter measures the potential difference between two points.

Connecting a Voltmeter

A voltmeter is connected in parallel across the component being measured.

For example, to measure the voltage across a resistor, connect one voltmeter lead to each side of the resistor.

 

 

 

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The voltmeter compares the electric potential at the two ends of the component.

It does not need to be placed directly in the main current path.

Why Is a Voltmeter Connected in Parallel?

A voltmeter measures the difference in electric potential between two points.

It therefore needs to be connected to the two points being compared.

An ideal voltmeter has:

extremely high resistance

This means very little current passes through it.

As a result, the voltmeter has very little effect on the circuit being measured.

Ammeter vs Voltmeter

A useful rule is:

Ammeter → series

Voltmeter → parallel

Using a Digital Multimeter

A digital multimeter can usually measure:

• DC voltage
• AC voltage
• current
• resistance
• continuity

Some models can also measure:

• capacitance
• frequency
• temperature
• diode voltage

The meter must be configured correctly before making a measurement.

 

 

 

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Connecting the Multimeter Leads

A typical multimeter has several sockets.

The black lead is usually connected to:

COM

The red lead may be connected to a socket labelled something similar to:

V/Ω

when measuring voltage or resistance.

For larger currents, the red lead may need to be moved to a dedicated current socket such as:

A

or:

10 A

The exact arrangement depends on the meter, so the instrument's labels and instructions should always be checked.

Selecting the Correct Measurement Mode

Before connecting the meter, identify what you are trying to measure.

If measuring voltage, select:

V

If measuring current, select:

A

If measuring resistance, select:

Ω

Many meters also distinguish between:

DC

and:

AC

Using the wrong setting can produce incorrect readings and, in some situations, damage the meter.

Selecting a Safe Range

Some meters require the user to select a measurement range.

If the expected value is unknown, begin with the highest suitable range.

Then reduce the range if necessary to obtain better precision.

For example, if measuring an unknown current, it is safer to begin on a higher current range rather than immediately selecting a very small range.

Autoranging meters perform much of this process automatically.

Measuring DC Voltage

To measure the voltage across a resistor:

1. Build the circuit.
2. Select DC voltage on the meter.
3. Connect the black lead to COM.
4. Connect the red lead to the voltage socket.
5. Connect the voltmeter in parallel across the resistor.
6. Switch on the circuit.
7. Read and record the voltage.

For a DC circuit, reversing the leads may cause a digital meter to display a negative value.

For example:

−6.02 V

usually means the leads are reversed relative to the chosen polarity.

Measuring Current Safely

To measure current:

1. Switch off the circuit.
2. Select the current function.
3. Check the correct meter socket.
4. Select a suitable current range.
5. Break the circuit at the desired measurement point.
6. Insert the meter in series.
7. Check all connections.
8. Switch on the circuit.
9. Record the reading.
10. Switch off before changing the circuit.

 

 

 

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This procedure reduces the risk of accidentally short-circuiting the supply.

Measuring Resistance

A multimeter can also measure resistance directly.

However, resistance should normally be measured with the component disconnected from an energized circuit.

To measure a resistor:

1. Switch off and disconnect the power.
2. Isolate the resistor where necessary.
3. Select Ω.
4. Connect the probes across the resistor.
5. Record the reading.

Never use the resistance setting to measure a powered circuit unless the instrument is specifically designed for such a procedure.

Measuring Current in a Series Circuit

Current should be the same at every point in a simple series circuit.

Suppose measurements give:

I₁ = 0.42 A

I₂ = 0.41 A

I₃ = 0.42 A

The readings are not perfectly identical, but they are very close.

The results support the theoretical prediction:

I₁ ≈ I₂ ≈ I₃

Small differences can result from measurement uncertainty.

Measuring Voltage in a Series Circuit

In a series circuit:

V_supply = V₁ + V₂ + V₃ + ...

Suppose measurements are:

V_supply = 10.0 V

V₁ = 3.1 V

V₂ = 6.8 V

Then:

V₁ + V₂ = 3.1 + 6.8

V₁ + V₂ = 9.9 V

This is very close to the measured supply voltage of 10.0 V.

The results support the theoretical model.

Measuring a Parallel Circuit

In a parallel circuit, theory predicts:

V_supply ≈ V₁ ≈ V₂ ≈ V₃

and:

I_total ≈ I₁ + I₂ + I₃

Suppose:

I_total = 0.75 A

I₁ = 0.50 A

I₂ = 0.24 A

Then:

I₁ + I₂ = 0.74 A

This is very close to:

I_total = 0.75 A

The small difference may be explained by experimental uncertainty.

 

 

 

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Using Measurements to Calculate Resistance

If voltage and current are measured, resistance can be calculated using:

R = V/I

Suppose:

V = 6.0 V

I = 0.30 A

Then:

R = 6.0/0.30

R = 20 Ω

This calculated resistance can then be compared with the labelled or directly measured resistance of the component.

Recording Measurement Data

Experimental measurements should be organized clearly.

For example:

The calculated resistance remains approximately constant.

This suggests that the component behaves approximately as an ohmic conductor over this range.

Appropriate Units

Always include units with measured values.

Common units include:

• voltage → V
• current → A
• resistance → Ω

Smaller or larger units may also be used:

1 mA = 0.001 A

1 μA = 0.000001 A

1 kΩ = 1000 Ω

1 MΩ = 1,000,000 Ω

Incorrect unit conversion is a common source of experimental error.

Resolution of a Measuring Instrument

Resolution is the smallest change that an instrument can display or distinguish.

For example, if a digital voltmeter displays:

5.27 V

and changes in steps of 0.01 V, its resolution is:

0.01 V

A meter with finer resolution can display smaller differences.

However, greater resolution does not automatically guarantee greater accuracy.

Accuracy

Accuracy describes how close a measured value is to the accepted or true value.

Suppose a known reference voltage is:

5.00 V

Meter A reads:

5.01 V

Meter B reads:

5.42 V

Meter A is more accurate in this situation.

Precision

Precision describes how closely repeated measurements agree with one another.

For example:

4.81 V

4.82 V

4.81 V

4.82 V

These measurements are very consistent and therefore precise.

However, measurements can be precise without being accurate.

Repeat Measurements

Repeating measurements helps identify random variation.

Suppose current is measured three times:

0.48 A

0.50 A

0.49 A

The mean is:

mean = (0.48 + 0.50 + 0.49)/3

mean = 1.47/3

mean = 0.49 A

Repeating measurements and calculating a mean can improve the reliability of experimental results.

Common Measurement Errors

Electrical measurements can be affected by several types of error.

Common examples include:

• incorrect meter connection
• incorrect meter range
• incorrect lead socket
• loose connections
• poor electrical contacts
• meter calibration errors
• resistance of connecting wires
• temperature changes
• reading errors
• power-supply fluctuations
• resistor tolerances

Recognizing these sources of error is an important part of evaluating an experiment.

Connecting an Ammeter Incorrectly

One of the most serious mistakes is connecting an ammeter in parallel across a component or power supply.

Because an ammeter has very low internal resistance, this may create a near-short circuit.

The resulting current may be very large.

This can:

• blow the meter fuse
• damage the circuit
• overheat wires
• damage the power source

Always check the circuit before switching it on.

Connecting a Voltmeter Incorrectly

A voltmeter connected in series has very high resistance.

This can greatly reduce the circuit current.

As a result, the circuit may behave very differently from its intended operation.

Therefore:

voltmeter → parallel

not series.

Wrong Meter Socket

A common multimeter error occurs when the red probe is left in the current socket after measuring current.

If the user then tries to measure voltage without moving the probe, the meter may effectively create a very low-resistance path.

This can blow the meter's fuse or create an unsafe condition.

Before every measurement, check:

• function
• range
• probe sockets
• circuit connection

Temperature as a Source of Error

Resistance can change with temperature.

If a resistor heats up during an experiment:

R may change

This can affect current and voltage measurements.

For many metallic conductors:

temperature increases → resistance increases

Therefore, taking measurements quickly or allowing the component to cool between trials may improve consistency.

Contact and Wire Resistance

Real wires do not have exactly zero resistance.

Connections between wires, clips and components can also introduce contact resistance.

This can cause measured values to differ slightly from simple theoretical calculations.

Loose or corroded connections can increase these effects.

 

 

 

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Instrument Loading

Measuring instruments can slightly affect the circuit they are measuring.

An ideal ammeter has:

R = 0 Ω

but a real ammeter has a small resistance.

An ideal voltmeter has:

R → extremely large

but a real voltmeter has a finite resistance.

Therefore, real instruments can change the circuit slightly.

This effect is sometimes called loading.

Comparing Experimental and Theoretical Results

Suppose theory predicts:

I_theoretical = 0.500 A

Experiment gives:

I_experimental = 0.485 A

The difference is:

|0.485 − 0.500| = 0.015 A

A percentage difference can be calculated:

percentage difference = |experimental − theoretical| / theoretical × 100%

Therefore:

percentage difference = 0.015/0.500 × 100%

percentage difference = 3.0%

This gives a useful numerical measure of how closely the experiment agrees with theory.

Evaluating an Experimental Result

A good evaluation should go beyond saying:

"The experiment worked."

Instead, consider:

• Did the measurements follow the predicted pattern?
• How close were experimental and theoretical values?
• Were measurements repeated?
• Were there any anomalous results?
• What was the instrument resolution?
• What sources of uncertainty were present?
• Did the apparatus affect the circuit?
• How could the experiment be improved?

This produces a much stronger scientific evaluation.

Anomalous Results

An anomalous result is a measurement that differs significantly from the general pattern.

Suppose current measurements are:

0.31 A

0.32 A

0.30 A

0.79 A

0.31 A

The 0.79 A result is clearly unusual.

Before simply removing it, investigate possible causes such as:

• loose connection
• incorrect meter range
• recording mistake
• temporary short circuit
• unstable power supply

The measurement should ideally be repeated.

Reliability

An experiment is more reliable when repeated measurements give similar results.

Reliability can be improved by:

• repeating measurements
• calculating mean values
• using consistent procedures
• controlling relevant variables
• checking connections between trials

One measurement alone provides less evidence than several consistent measurements.

Improving Accuracy

Possible improvements include:

• using calibrated instruments
• selecting an appropriate meter range
• using equipment with suitable resolution
• ensuring secure electrical contacts
• checking the power supply voltage
• reducing unwanted heating
• using low-resistance connecting wires
• repeating measurements

The best improvement depends on the main source of uncertainty in the experiment.

Improving Precision

Precision can often be improved by:

• using higher-resolution equipment
• keeping conditions constant
• repeating measurements
• using stable connections
• avoiding unnecessary movement of equipment
• taking readings consistently

Remember:

precision and accuracy are not the same thing.

Experimental Test of Ohm's Law

A common electrical experiment investigates the relationship between voltage and current.

A circuit might contain:

• power supply
• resistor
• ammeter
• voltmeter
• variable resistor
• switch

 

 

 

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The voltage is changed and corresponding current readings are recorded.

If:

V/I ≈ constant

the component behaves approximately as an ohmic conductor under those conditions.

Example Experimental Data

The resistance values are not perfectly identical.

However, they are reasonably close to:

10 Ω

The small differences are consistent with normal experimental uncertainty.

Therefore, the data provide evidence that the resistor behaves approximately ohmically.

Interpreting Data Patterns

When analyzing measurement data, look for:

• increasing or decreasing trends
• proportional relationships
• constant quantities
• anomalous values
• agreement with theory
• systematic differences

For example, if doubling voltage approximately doubles current, this supports:

V ∝ I

If V/I remains approximately constant, the resistance is approximately constant.

Systematic Error

A systematic error shifts measurements consistently in the same direction.

For example, suppose a voltmeter always reads 0.20 V too high.

A true voltage of:

5.00 V

would be measured as:

5.20 V.

Repeating the measurement many times would not remove this error.

The instrument would need to be checked or calibrated.

Random Error

Random errors cause measurements to vary unpredictably.

For example:

2.98 V

3.03 V

3.00 V

2.96 V

3.02 V

Repeating measurements and calculating a mean can reduce the effect of random variation.

This is different from a systematic error, which consistently biases the results.

Safe Laboratory Practice

When working with school electrical circuits:

• use the low-voltage supplies provided
• switch off power before changing connections
• check the meter setting before connecting it
• begin with an appropriate safe range
• never short-circuit the power supply
• avoid touching exposed conductors unnecessarily
• stop if components become unusually hot
• check polarity where appropriate
• follow the equipment manufacturer's instructions

These practices protect both the equipment and the person carrying out the experiment.

A Useful Meter Checklist

Before switching on:

What am I measuring?

Current or voltage?

Is the meter set correctly?

A or V?

Are the leads in the correct sockets?

Especially check the current socket.

Is the meter connected correctly?

Ammeter → series

Voltmeter → parallel

Is the range appropriate?

Begin safely if the value is unknown.

Are the connections secure?

Then switch on and take the measurement.

Common Mistakes

Mistake: Connecting an ammeter in parallel.
Ammeters are normally connected in series.

Mistake: Connecting a voltmeter in series.
Voltmeters are connected in parallel.

Mistake: Forgetting to move the multimeter lead after measuring current.
Always check the probe sockets before changing measurement type.

Mistake: Using the wrong range.
A range that is too small may overload the meter; an unnecessarily large range may reduce useful precision.

Mistake: Ignoring units.
0.25 A is not the same as 0.25 mA.

Mistake: Assuming experimental results must exactly match theoretical values.
Real measurements always contain uncertainty.

Mistake: Calling every difference a "human error."
Identify a specific source, such as contact resistance, meter resolution or temperature change.

Mistake: Removing anomalous results without investigation.
Repeat the measurement and look for a possible cause.

Mistake: Confusing accuracy with precision.
Accurate results are close to the accepted value; precise results are closely grouped.

Key Terms

Ammeter — instrument used to measure electric current.

Voltmeter — instrument used to measure potential difference.

Multimeter — instrument capable of measuring several electrical quantities.

Current — rate of flow of electric charge.

Potential difference — energy transferred per unit charge.

Resistance — opposition to electric current.

Series connection — connection in which current passes through components along the same path.

Parallel connection — connection in which components are connected between the same two electrical points.

Resolution — smallest change an instrument can distinguish or display.

Accuracy — closeness of a measured value to the accepted or true value.

Precision — closeness of repeated measurements to one another.

Uncertainty — estimated range associated with a measured value.

Random error — unpredictable variation between measurements.

Systematic error — consistent bias affecting measurements in the same direction.

Anomalous result — result that differs substantially from the general pattern.

Reliability — degree to which repeated measurements produce consistent results.

Instrument loading — change to a circuit caused by the measuring instrument itself.

Key Takeaways

• Ammeters measure current and are normally connected in series.
• Voltmeters measure potential difference and are connected in parallel.
• Ammeters are designed to have very low resistance.
• Voltmeters are designed to have very high resistance.
• A multimeter must be set to the correct function, range and probe sockets.
• Never connect an ammeter directly across a power source.
• Switch off the circuit before changing connections.
• Start with a safe measurement range when the expected value is uncertain.
• Current measurements can be used to test series and parallel circuit rules.
• Voltage measurements can be used to test energy relationships in circuits.
• Resistance can be calculated from measured voltage and current using R = V/I.
• Experimental measurements rarely match theoretical values perfectly.
• Resolution, accuracy and precision describe different aspects of measurement quality.
• Repeated measurements improve reliability and help identify anomalous results.
• Random errors can often be reduced through repetition and averaging.
• Systematic errors require identification and correction rather than simple repetition.
• Contact resistance, wire resistance, temperature and meter properties can affect measurements.
• Experimental results should be evaluated by comparing them quantitatively with theoretical predictions.
• A strong evaluation identifies specific limitations and realistic improvements.

Check Your Understanding

1. What quantity does an ammeter measure?
2. How should an ammeter be connected in a circuit?
3. What quantity does a voltmeter measure?
4. How should a voltmeter be connected?
5. Explain why an ammeter has very low internal resistance.
6. Explain why a voltmeter has very high internal resistance.
7. Why can connecting an ammeter directly across a power supply be dangerous?
8. What should you check before using a digital multimeter to measure current?
9. Why is it sensible to begin with a higher measurement range when the expected value is unknown?
10. A voltmeter displays −4.8 V in a DC circuit. What might this indicate?
11. Convert 250 mA to amperes.
12. A resistor has 6.0 V across it and carries 0.30 A. Calculate its resistance.
13. Three current measurements are 0.48 A, 0.50 A and 0.49 A. Calculate the mean current.
14. Explain the difference between accuracy and precision.
15. Explain the difference between random and systematic error.
16. Give three possible reasons why an experimental circuit measurement may differ from a theoretical prediction.
17. A theoretical current is 0.400 A and the experimental current is 0.388 A. Calculate the percentage difference.
18. Explain why repeated measurements are useful.
19. Describe how you could experimentally test whether current is the same throughout a series circuit.
20. Describe how you could use ammeters and voltmeters to test the theoretical rules for a parallel circuit.