Potential difference and resistance

Potential difference

The current through a component depends on both the resistance of the component and the potential difference across the component.

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Potential difference is a measure of how much energy is transferred between two points in a circuit.
Circuit with a cell, switch and lamp. A voltmeter is connected in parallel with the lamp.

Measuring potential difference

To measure the potential difference across a component, a voltmeter must be placed in parallel with that component in order to measure the difference in energy from one side of the component to the other. Potential difference is also known as voltage and is measured in volts (V).

Energy, voltage and charge

When a charge moves through a potential difference, electrical work is done and energy transferred. The energy transferred can be calculated using the equation:

Energy transferred = charge moved × potential difference

E = Q \times V

This is when:

  • potential difference (V) is measured in volts (V)
  • energy (E) is measured in joules (J)
  • charge (Q) is measured in coulombs (C)

One volt is the potential difference when one coulomb of charge transfers one joule of energy.

Example

What is the potential difference between two points if 2 C of charge shifts 4 J?

V = \frac{E}{Q}

V = \frac{4}{2}

V = 2 \ V

Question

How much energy is transferred when 3 C of charge moves through a potential difference of 6 V?

E = V \times Q

E = 6 \times 3

E = 18 \ J

Resistance

When a charge moves through a potential difference, electrical work is done and energy transferred. The potential difference can be calculated using the equation:

potential difference = current × resistance

V = I \times R

This is when:

  • potential difference (V) is measured in volts (V)
  • current (I) is measured in amps (A)
  • resistance (R) is measured in ohms (Ω)

From the equation, it can be seen that increasing the resistance for a certain potential difference will reduce the current passing through. For example, if a variable resistor is adjusted to double its initial resistance, the current passing will be halved.

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Conductors have a low resistance. Insulators have large resistances.

Example

What is the potential difference if a current of 2 A flows through a resistance of 40 Ω?

V = I \times R

V = 2 \times 40

V = 80 \ V

Question

What is the resistance of a component if 12 V causes a current of 2 A through it?

V = I \times R

R = \frac{V}{I}

R = \frac{12}{2}

R = 6 \ Ω