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ELECTRICITY · CHAPTER 10 OF 13

Resistance

Current does not flow equally easily through every component. Resistance describes how strongly a component opposes the flow of charge.

By the end, you’ll be able to…

  • Describe resistance as opposition to the flow of current.
  • Use the equation V = I × R.
  • Explain how resistance affects the current in a circuit.

Why does higher resistance mean a smaller current?

As electrons move through a metal, they interact with the metal lattice. Greater resistance means their overall drift through the wire is more strongly opposed. The electrons therefore make slower overall progress, so less charge passes a point each second. This means the current is smaller.

LOWER RESISTANCE Charge flows more easily
− − − − −
− Moving electron + Positive ion in the metal lattice

The electrons move through the spaces in the metal lattice with an overall drift, so charge passes along the wire.

HIGHER RESISTANCE Charge flow opposed more strongly
− − − − −
− Moving electron + Positive ion in the metal lattice

The electrons still move through the metal lattice, but their overall drift is slower, so less charge passes a point each second.

Why does higher resistance mean a smaller current?
As electrons move through a metal, they interact with the metal lattice. Greater resistance means their overall drift through the wire is more strongly opposed. The electrons therefore make slower overall progress, so less charge passes a point each second. This means the current is smaller.

☆ Resistance does not use up charge. The charges still move around the complete circuit. A resistor transfers electrical energy to the surroundings, often by heating.

INTERACTIVE SIMULATION

What happens when resistance increases?

The cell provides a constant potential difference of 6 V. Change only the resistance and watch the current, charge flow and bulb brightness.

Select a resistance on the scale and observe how the current, electron drift and bulb brightness change.
RESISTANCE INVESTIGATION
Resistance
2 Ω 4 Ω 6 Ω 8 Ω 12 Ω
lower resistance higher resistance
A6 V CELLVARIABLE RESISTORBULB − − − − − − − − − −
POTENTIAL DIFFERENCE 6.0 V
RESISTANCE 2 Ω 4 Ω 6 Ω 8 Ω 12 Ω
CURRENT 3.00 A 1.50 A 1.00 A 0.75 A 0.50 A
Current is large. The resistance is low, so the overall electron drift is greater and the bulb is bright.
Current is relatively large. With a resistance of 4 Ω, the current is 1.50 A.
Current has decreased. Increasing the resistance reduces the current even though the potential difference stays at 6 V.
Current is smaller. The greater resistance produces a smaller current and the bulb becomes dimmer.
Current is relatively small. At the highest resistance, the overall electron drift is smallest and the bulb is dim.

What does the simulation show?
The potential difference stays at 6 V while the resistance changes. As resistance increases, the current decreases: the electrons have a slower overall drift, so less charge passes a point each second. The bulb also becomes dimmer because a smaller current flows through it.

Same potential difference → higher resistance → smaller current

CALCULATING RESISTANCE
Compare potential difference with current

When current flows through a component with resistance, electrical energy is transferred to its thermal energy store. The power transferred depends on both the current and the resistance.

The equation

resistance = potential difference ÷ current

R = V ÷ I

R= resistance in ohms (A)

V=potential difference in volts (V)

I=current in amps (A)

To calculate resistance:

R = V÷ I

A resistor has a potential difference of 6 V across it and a current of 2 A.

R = V÷ I

R = 6 ÷ 2

R= 3 Ω

To calculate potential difference:

V = I x R

A resistor has a resistance of 4 Ω and a current of 1.5 A.

V = I x R

V = 1.5 × 4

V= 6 V

To calculate current:

I = V÷ R

A 6 Ω resistor has a potential difference of 12 V across it.

I = V÷ R

I = 12 ÷ 6

I= 2 A

INTERACTIVE PRACTICE

Can you hit the target?

Use the relationship between potential difference, current and resistance to make the circuit behave as required.

Select a question, then choose the answer that hits the target.
V = I × R PRACTICE Choose a question
TARGET CURRENT: 1.5 A

Which resistor will hit the target?

The potential difference is 6 V. Choose the resistance that will produce a current of 1.5 A.

A6 V CHOOSE R
Not quite. With only 2 Ω of resistance, I = 6 ÷ 2 = 3 A.
Correct. I = V ÷ R = 6 ÷ 4 = 1.5 A.
Not quite. 8 Ω gives I = 6 ÷ 8 = 0.75 A.
TARGET CURRENT: 2.0 A

Choose the resistance

The supply is 12 V. Which resistor will produce a current of 2.0 A?

Not quite. 12 ÷ 3 = 4 A, so the current would be too large.
Correct. R = V ÷ I = 12 ÷ 2 = 6 Ω.
Not quite. 12 ÷ 12 = 1 A, so the current would be too small.
TARGET POTENTIAL DIFFERENCE

What supply is needed?

A 4 Ω resistor needs a current of 1.5 A. Which potential difference will produce it?

Not quite. Use V = I × R. Multiply 1.5 by 4.
Correct. V = I × R = 1.5 × 4 = 6 V.
Not quite. Use V = I × R. Multiply 1.5 by 4.
PREDICT THE AMMETER

What will the ammeter read?

The circuit has a potential difference of 9 V and a resistance of 6 Ω.

Not quite. Current is potential difference divided by resistance.
Correct. I = V ÷ R = 9 ÷ 6 = 1.5 A.
Not quite. Current is potential difference divided by resistance. Try 9 ÷ 6.
FIX THE CIRCUIT

Reduce the current

The cell provides a constant potential difference of 6 V. The ammeter reading is too high, so the bulb is brighter than required. How should the variable resistor be adjusted to reduce the current?

POTENTIAL DIFFERENCE 6 V CURRENT NOW 3.0 A TARGET CURRENT 1.5 A
A3.04.51.56 V CELL VARIABLE RESISTOR BULB − − − − − −
Current is above the target. Current has increased further. Target current reached.
Not quite. Decreasing the resistance makes it easier for charge to flow, so the current becomes even larger.
Correct. Increasing the resistance makes it more difficult for charge to flow. Because the potential difference remains at 6 V, the current decreases.
Not quite. The resistance must increase to reduce the current while the potential difference stays constant.
RESISTANCE OF A WIRE
Length, thickness and temperature matter

⟷ A longer wire

Charges travel farther through the metal lattice, so their overall motion is opposed more strongly, leading to a higher resistance.

◯ A thicker wire

A thicker wire has a lower resistance. There is a larger cross-sectional area for charge to flow through.

🌡️A hotter metal wire

usually has a higher resistance. Its ions vibrate more, causing more collisions.

Investigating the resistance of a wire

You may be asked to investigate how the length of a wire affects its resistance.

  1. Build a circuit with the test wire and an ammeter in series.
  2. Connect a voltmeter in parallel across the test wire.
  3. Measure the potential difference and current, then calculate R = V ÷ I.
  4. Repeat for different lengths of wire, keeping the material and thickness the same.

Safety: Switch off the circuit between readings to reduce heating. A hotter wire has a different resistance

INTERACTIVE INVESTIGATION

How do different components behave?

Explore how potential difference, temperature and light intensity affect different resistive components.

Select a component, then move the slider to change the condition and watch what happens.

Fixed resistor

At a constant temperature, its resistance stays approximately constant. Increasing the potential difference increases the current, but the resistance stays approximately the same.

Move the slider to change the potential difference
CHARGE FLOW Slower Medium Faster
− − − − − − − −
RESISTANCE Approximately constant
potential difference rises → current rises → resistance stays approximately constant

Filament lamp

As the filament gets hotter, its resistance increases. The greater resistance means the overall drift of charge becomes slower.

Move the slider to change the filament temperature
CHARGE FLOW Faster Medium Slower
− − − − − − − −
RESISTANCE Lower Medium Higher
hotter filament → higher resistance → smaller current

Thermistor

In the type of thermistor used at GCSE, resistance decreases as temperature increases.

Move the slider to change the temperature
CHARGE FLOW Slower Medium Faster
− − − − − − − −
RESISTANCE Higher Medium Lower
temperature rises → resistance falls → current increases
↘ ↘ ↘ ↘ ↘

LDR

An LDR responds to light. Its resistance decreases as the light intensity increases.

Move the slider to change the light intensity
CHARGE FLOW Slower Medium Faster
− − − − − − − −
RESISTANCE Higher Medium Lower
light intensity rises → resistance falls → current increases
Remember the two sensors
Thermistor: hotter → lower resistance LDR: brighter → lower resistance
INTERACTIVE QUICK CHECK

Check your understanding

Answer all three questions about resistance.

Select one answer for each question. You will get feedback straight away.
1 A 12 Ω resistor and a 4 Ω resistor are each connected across the same potential difference. Which has the larger current?
2 A resistor has a potential difference of 6 V across it and a current of 2 A. What is its resistance?
3 What happens to the resistance of an LDR when the light intensity increases?
INTERACTIVE CHALLENGE

Why should a wire be switched off between resistance readings?

Think about how current affects the wire’s temperature, then reveal the answer.

Current heats the wire. A hotter metal wire has a greater resistance, so allowing its temperature to change would make the investigation unfair.

CHAPTER 10

Chapter summary

  • Resistance describes how strongly a component opposes the current and is measured in ohms (Ω).
  • Resistance can be calculated using R = V ÷ I.
  • For the same potential difference, a higher resistance produces a smaller current.
  • The resistance of a wire depends on its length, thickness and temperature.
  • The resistance of a thermistor decreases as temperature increases, while the resistance of an LDR decreases as light intensity increases.

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09 · Measuring potential difference

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11 · Series and parallel circuits