Define current, potential difference and resistance, apply Ohm's law V = IR, and analyse series and parallel circuits and electrical power

What this dot point is asking

SEAB wants you to define current, potential difference and resistance, to apply Ohm's law $V = IR$, and to work out currents, voltages and resistances in simple series and parallel circuits, plus electrical power. The calculations are short divisions and additions; the marks come from the definitions, the circuit rules, and keeping current in amperes.

The answer

Current, potential difference and resistance

• Current ($I$) is the rate of flow of electric charge, measured in amperes ($\text{A}$).
• Potential difference, or voltage ($V$), is the energy transferred per unit charge, measured in volts ($\text{V}$); it is what drives the current.
• Resistance ($R$) opposes the flow of current, measured in ohms ($\Omega$).

Ohm's law

For a metal conductor at constant temperature, the current is proportional to the voltage:

A higher resistance gives a smaller current for the same voltage. Rearranged, $I = V/R$ and $R = V/I$.

Series circuits

In a series circuit the components are in one loop:

• the current is the same everywhere,
• the voltages across the components add up to the supply voltage,
• the total resistance is the sum: $R = R_1 + R_2 + \dots$

Parallel circuits

In a parallel circuit components are on separate branches:

• the voltage across each branch is the same,
• the branch currents add up to the total current,
• adding more parallel branches lowers the total resistance.

Electrical power and energy

The power transferred by a component is:

measured in watts. The electrical energy used is $E = Pt = VIt$, in joules. This is why a higher-power appliance costs more to run for the same time.

Examples in context

Example 1. House wiring is parallel. Lights and sockets are wired in parallel so each receives the full mains voltage and can be switched independently. If they were in series, switching one off would break the loop and turn them all off, and each would receive only a share of the voltage.

Example 2. A dimming torch. As a torch battery runs down, its voltage falls. By Ohm's law the current through the bulb drops for the same resistance, so the bulb dissipates less power ($P = VI$) and glows more dimly.

Try this

Q1. Define electric current and give its unit. [2 marks]

• Cue. Current is the rate of flow of electric charge; its unit is the ampere ($\text{A}$).

Q2. A $9.0\ \text{V}$ supply drives a current of $0.30\ \text{A}$ through a resistor. Find its resistance. [2 marks]

• Cue. $R = \dfrac{V}{I} = \dfrac{9.0}{0.30} = 30\ \Omega$.

Q3. Explain why the total resistance falls when a second resistor is added in parallel. [2 marks]

• Cue. The extra branch gives the current more paths to flow through, so more total current flows for the same voltage, which means a lower overall resistance.