Define voltage and resistance, and use V = I times R and electrical power P = V times I

What this dot point is asking

SEAB wants you to define voltage and resistance, to use Ohm's law $V = IR$ to link voltage, current and resistance, and to calculate electrical power with $P = VI$. The big idea is that voltage pushes current through a circuit, resistance opposes that current, and the three are tied together by one simple law.

The answer

Voltage

Voltage (also called potential difference) is the energy given to each unit of charge by the source, or the energy transferred by each unit of charge in a component. It is what pushes the current around a circuit. Voltage is measured in volts ($\text{V}$) using a voltmeter connected across (in parallel with) a component.

A bigger voltage pushes a bigger current through the same component.

Resistance

Resistance is how much a component opposes the flow of current. A high resistance lets only a small current through for a given voltage. Resistance is measured in ohms ($\Omega$).

Resistance is defined by:

so resistance is the voltage across a component divided by the current through it. Thin wires, long wires and poor conductors have higher resistance.

Ohm's law

Ohm's law states that the current through a metal conductor is directly proportional to the voltage across it, provided its temperature stays constant. This gives the equation:

You can rearrange it three ways: $V = IR$ to find voltage, $I = \dfrac{V}{R}$ to find current, and $R = \dfrac{V}{I}$ to find resistance.

For a component that obeys Ohm's law, a graph of current against voltage is a straight line through the origin.

Electrical power

Electrical power is the rate at which a component transfers electrical energy, for example into heat and light. It is given by:

where $P$ is the power in watts, $V$ is the voltage in volts, and $I$ is the current in amps. A device with a high power rating, such as a kettle, transfers a lot of energy each second.

Examples in context

Example 1. A dimmer switch. A dimmer increases the resistance in series with a lamp. By Ohm's law, more resistance means a smaller current for the same supply voltage, so less power is transferred ($P = VI$) and the lamp shines less brightly. Turning the dimmer the other way lowers the resistance and brightens the lamp.

Example 2. Why thick cables for high power. Appliances that draw a large current, such as an electric cooker, need thick connecting cables. Thick wires have a low resistance, so they do not overheat as the large current passes. A thin wire would have a higher resistance and could get dangerously hot.

Try this

• Cue. A $9.0\ \text{V}$ battery drives a current of $3.0\ \text{A}$ through a resistor. Find the resistance. [2 marks] $R = \dfrac{V}{I} = \dfrac{9.0}{3.0} = 3.0\ \Omega$.

• Cue. A current of $0.50\ \text{A}$ flows through a $20\ \Omega$ resistor. Find the voltage across it. [2 marks] $V = IR = 0.50 \times 20 = 10\ \text{V}$.

• Cue. A device runs at $230\ \text{V}$ and draws $2.0\ \text{A}$. Find its power. [2 marks] $P = VI = 230 \times 2.0 = 460\ \text{W}$.