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AQA PhysicsElectricity

Current, potential difference and resistance

Use circuit equations and explain electrical resistance.

Start here

The key idea

Current is the rate of flow of charge. Potential difference transfers energy per unit charge.

Equation to know

potential difference = current x resistance

Current Potential Difference And Resistance
VIRpotential difference = current x resistance

Use the labels to explain the scientific relationship shown.

Revision notes

The bit that matters

Short notes first. Learn the idea, then use the worked example and questions to check it properly.

1

Current and charge

Electric current is the rate of flow of electric charge.Charge flow = current x time, written Q = I x t, with charge in coulombs (C), current in amperes (A) and time in seconds (s).Current only flows in a closed circuit and is the same at every point in a single loop (series), because charge is conserved.Current is measured with an ammeter connected in series.

2

Potential difference

Potential difference (voltage) is the energy transferred per unit charge passing between two points. d. in volts (V).It is measured with a voltmeter connected in parallel across a component.

3

Resistance and Ohm's law

Resistance opposes the flow of current and is measured in ohms.Potential difference = current x resistance, written V = I x R.For an ohmic conductor at constant temperature, current is directly proportional to potential difference, so resistance is constant and the I-V graph is a straight line through the origin.

4

Non-ohmic components

A filament lamp is non-ohmic: as current increases the filament heats up, its resistance increases, and the I-V graph curves.A diode allows current to flow in one direction only, so it has very high resistance in reverse.A thermistor's resistance falls as temperature rises, and a light-dependent resistor's (LDR) resistance falls as light intensity rises.

Key terms

Definitions to learn

Current

The rate of flow of electric charge, measured in amperes.

Potential difference

Energy transferred per unit charge, measured in volts.

Resistance

The opposition to current flow, measured in ohms.

Ohmic conductor

A component whose resistance stays constant at fixed temperature.

Coulomb

The unit of charge; one coulomb passes when 1 A flows for 1 s.

Worked example

A resistor has a resistance of 15 ohms and a current of 0.40 A. Calculate the potential difference.

1

Use V = IR.

2

Substitute V = 0.40 × 15.

Final answer

6.0 V

Exam habit

State the equation before substituting.For ohm's law questions, identify which two quantities are given and rearrange V = IR accordingly.Always include units — volts, amps and ohms.

Watch out

Do not use the total circuit current blindly in a parallel branch.

Examiner tips

How to score full marks

  • 1Ammeters go in series; voltmeters go in parallel across the component.
  • 2For an ohmic conductor, resistance is constant only if temperature is constant.
  • 3Rearrange V = I x R carefully: R = V / I and I = V / R.
Quick-fire quiz

Test yourself

Pick an answer — you'll see instantly if it's right.

A resistor has a potential difference of 6 V and a current of 0.2 A. What is its resistance?

Which quantity is measured in amperes?

A 12 Ω resistor carries a current of 0.5 A. What is the potential difference across it?

Why does the resistance of a filament lamp increase as it gets hotter?

A current of 2 A flows for 5 minutes. How much charge is transferred?

Practice questions

Try these yourself

Start with the core skill, then open the answer only after you have attempted the full question.

1A component has a potential difference of 12 V and a current of 0.50 A. Find its resistance.
Mark scheme
  1. 1.Use R = V / I.
24 ohms
2Calculate the charge transferred by a current of 0.30 A in 4 minutes.
Mark scheme
  1. 1.Convert minutes to seconds.
  2. 2.Use Q = It.
72 C
3Explain why the resistance of a filament lamp increases as it gets hotter.
Mark scheme
  1. 1.Think about the metal ions and electron collisions.
The ions vibrate more, causing more collisions with electrons and increasing resistance.
4State the equation linking charge flow, current and time.[1 mark]
Mark scheme
  1. 1.Charge depends on how much current flows and for how long.
charge = current x time (Q = I x t) (1)
5A current of 3.0 A flows for 120 s. Calculate the charge that flows.[2 marks]
Mark scheme
  1. 1.Use Q = I x t.
  2. 2.Substitute I = 3.0 and t = 120.
Q = I x t (1) = 3.0 × 120 = 360 C (1)
6A resistor has a potential difference of 12 V across it and a current of 0.5 A. Calculate its resistance.[2 marks]
Mark scheme
  1. 1.Rearrange V = I x R to R = V / I.
  2. 2.Substitute V = 12 and I = 0.5.
R = V / I (1) = 12 / 0.5 = 24 ohms (1)
7Describe the shape of the I-V graph for an ohmic conductor and explain what it shows.[2 marks]
Mark scheme
  1. 1.Recall the proportionality.
  2. 2.Link the straight line to constant resistance.
The graph is a straight line through the origin (1); current is directly proportional to potential difference, which shows the resistance is constant (1)
8Explain why the resistance of a filament lamp increases as the current through it increases, and describe how this affects the I-V graph.[3 marks]
Mark scheme
  1. 1.Link current to heating.
  2. 2.Link temperature to ion vibration.
  3. 3.Connect higher resistance to graph shape.
As current increases the filament gets hotter (1); the metal ions vibrate more and collide more with the flowing electrons, increasing resistance (1); so for larger p.d. the current rises less steeply, giving an S-shaped curve rather than a straight line (1)
9A hairdryer operates at 230 V and its heating element has a resistance of 26.5 ohms. Calculate the current drawn.[3 marks]
Mark scheme
  1. 1.Rearrange V = I x R to I = V / R.
  2. 2.Substitute V = 230 and R = 26.5.
  3. 3.Evaluate and state unit.
I = V / R (1) = 230 / 26.5 (1) = 8.68 A (accept 8.7 A) (1)
10A charge of 180 C passes through a lamp and transfers 1800 J of energy. Calculate the potential difference across the lamp.[3 marks]
Mark scheme
  1. 1.Use E = Q x V.
  2. 2.Rearrange to V = E / Q.
  3. 3.Substitute E = 1800 and Q = 180.
V = E / Q (1) = 1800 / 180 (1) = 10 V (1)
11Explain how a thermistor can be used in a temperature-sensing circuit. Describe what happens to its resistance and current as temperature increases.[3 marks]
Mark scheme
  1. 1.State the relationship between temperature and resistance for a thermistor.
  2. 2.Explain the effect on current using V = I x R.
  3. 3.Describe a practical sensing application.
As temperature increases, the resistance of a thermistor decreases (1); if connected to a fixed supply, a lower resistance means a higher current flows (from I = V / R) (1); the change in current can be used to trigger a circuit, for example to switch on a fan or cooling system when temperature rises above a set level (1)
12An LDR and a fixed resistor of 1000 ohms are connected in series to a 6 V supply. In bright light the LDR has a resistance of 200 ohms; in the dark its resistance is 10 000 ohms. Calculate the current in each condition.[3 marks]
Mark scheme
  1. 1.Total resistance in bright light = 200 + 1000 = 1200 ohms.
  2. 2.I = V / R = 6 / 1200 for bright light.
  3. 3.Total resistance in dark = 10000 + 1000 = 11000 ohms.
  4. 4.I = 6 / 11000 for dark.
Bright light: R total = 200 + 1000 = 1200 ohms; I = 6 / 1200 = 0.005 A = 5 mA (1); Dark: R total = 10000 + 1000 = 11000 ohms; I = 6 / 11000 = 0.00055 A = 0.55 mA (1); the current is much larger in bright light because the LDR resistance is lower (1)
13A student sets up a circuit to investigate a diode. She finds that when the diode is connected in the forward direction a current of 0.20 A flows with a p.d. of 0.7 V. When reversed, the current is effectively zero even with 12 V applied. Calculate the resistance in the forward direction and explain the behaviour in the reverse direction.[3 marks]
Mark scheme
  1. 1.Forward resistance R = V / I = 0.7 / 0.20.
  2. 2.Explain that a diode only conducts in one direction.
  3. 3.Explain very high resistance in reverse direction.
R = V / I = 0.7 / 0.20 = 3.5 ohms (1); in the reverse direction the diode has extremely high resistance, so even though 12 V is applied, negligible current flows (1); the diode allows conventional current to flow in one direction only, which is why it is used to convert a.c. to d.c. (1)
14Explain, with reference to electron movement and ion vibration, why the resistance of a metal wire increases with temperature. Then suggest why engineers designing high-power cables choose materials with the lowest possible resistance coefficient.[4 marks]
Mark scheme
  1. 1.Metals have free electrons that carry charge.
  2. 2.At higher temperature, lattice ions vibrate more.
  3. 3.Increased vibration means more electron collisions and higher resistance.
  4. 4.Link lower resistance coefficient to less energy wasted as heat in cables.
In a metal, free electrons are the charge carriers; when they move through the lattice they collide with the positive ions (1); as temperature rises the ions vibrate with greater amplitude, increasing the frequency of these collisions and making it harder for electrons to flow, so resistance increases (1); engineers prefer materials with a low resistance temperature coefficient so that even when cables carry large currents and warm up, their resistance increases by only a small amount (1); a smaller resistance increase means less power wasted as heat in the cable (P = I2 x R), keeping transmission efficient and preventing overheating (1)
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