Describe how current and voltage divide in series and parallel circuits and find combined resistance

What this dot point is asking

SEAB wants you to describe how current and voltage behave in series and in parallel circuits, to find the combined resistance of resistors in series, and to explain why household circuits use parallel wiring. The big idea is that components joined in a single loop (series) share the voltage and pass the same current, while components on separate branches (parallel) each get the full voltage.

The answer

Series circuits

In a series circuit the components are joined one after another in a single loop, so there is only one path for the current.

• The current is the same at every point in the loop. There is only one path, so the charge that flows through one component must flow through them all.
• The voltage is shared between the components. The supply voltage equals the sum of the voltages across each component.
• Resistances add together: $R_{\text{total}} = R_1 + R_2 + \dots$

A drawback is that if one component breaks, the whole circuit stops, because the single path is broken. Old fairy lights wired in series all went out when one bulb failed.

Parallel circuits

In a parallel circuit the components are on separate branches, so there is more than one path for the current.

• Each branch has the full supply voltage across it. Every component gets the same voltage as the battery.
• The current divides between the branches and then recombines. The total current from the battery equals the sum of the currents in the branches.
• Adding more parallel branches lowers the total resistance, because there are more paths for the current.

An advantage is that each branch works on its own. If one branch breaks, the others keep working, and each can have its own switch.

Combined resistance in series

For resistors in series, simply add the values to get the combined resistance, then use Ohm's law for the whole circuit. (In parallel, the combined resistance is always less than the smallest single resistance, because the extra paths make it easier for current to flow.)

Why houses use parallel wiring

Household appliances and lights are connected in parallel so that:

• each one receives the full mains voltage and works properly;
• each can be switched on or off without affecting the others;
• one appliance failing does not switch off the rest.

Examples in context

Example 1. Christmas lights. Modern decorative lights are usually wired so that one bulb failing does not switch off the whole string, unlike the old series sets. Wiring lamps in parallel, or using special bulbs, means a single failure does not break the only path for the current.

Example 2. A car's electrics. A car wires its headlights, radio and wipers in parallel from the battery, so each gets the full battery voltage and can be switched independently. If they were in series, switching one off would cut the current to all of them, and each would only get a share of the voltage.

Try this

• Cue. Two $6.0\ \Omega$ resistors are connected in series. Find the combined resistance. [1 mark] In series they add: $6.0 + 6.0 = 12\ \Omega$.

• Cue. State how the voltage across each lamp compares with the supply for two lamps in parallel. [1 mark] Each lamp has the full supply voltage across it.

• Cue. Explain why the current is the same at every point in a series circuit. [2 marks] There is only one path, so the charge flowing through one component must flow through all of them; the current cannot build up or disappear.