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Parallel circuits

Electricity and magnetism · level 5, lesson 4 of 6

A question to start

In your home, you can switch off the kitchen light and the fridge keeps running. Why do the lights and plugs not all go off together, like fairy lights in a single loop?

The idea

Parts in parallel are on separate branches, each connected straight across the supply.

  • Every branch has the same voltage, the full supply voltage.
  • The branch currents add: \(I = I_1 + I_2 + \dots\)
  • The combined resistance is less than any single branch:
\[\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \dots\]

Each branch works on its own. Homes are wired in parallel, so each light and socket gets the full 120 V and can be switched separately.

6 Ω: 2 A3 Ω: 4 A12 Vtotal 6 A

Worked examples

1. The diagram. \(I_1 = 12/6 = 2\) A, \(I_2 = 12/3 = 4\) A, total 6 A. Combined: \(1/R = 1/6 + 1/3 = 1/2\), so \(R = 2\ \Omega\), and \(12/2 = 6\) A.

2. Two equal branches. Two 10 \(\Omega\) resistors in parallel: \(R = 5\ \Omega\), half of one.

3. A kitchen. A 1,500 W kettle (12.5 A) and a 1,200 W toaster (10 A) on the same 120 V circuit draw 22.5 A together, enough to trip a 15 A breaker.

Try it

  1. Find the combined resistance of 4 \(\Omega\) and 12 \(\Omega\) in parallel.
  2. They are put across 24 V. Find each branch current and the total.
  3. Why is a house wired in parallel?
  4. A third branch is added. Does the total current go up or down?
Answers
  1. \(1/R = 1/4 + 1/12 = 1/3\): \(R = 3\ \Omega\).
  2. 6 A and 2 A, total 8 A (and \(24/3 = 8\) A).
  3. Each appliance gets the full voltage and can be switched on and off on its own.
  4. Up: each branch adds its own current.

Common mistake

"More branches means more resistance." Each new branch is another path for the current, so the combined resistance goes down and the total current goes up.

Where it leads