Potential difference and resistance

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

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).

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

Energy, voltage and charge

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 = \frac{energy}{charge}

V = \frac{E}{Q}

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?

V = \frac{E}{Q}

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)

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

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Conductors have a low resistance. Insulators have a high resistance.

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