Topic 4 of 5

Parallel circuits

In a parallel circuit each component has its own branch across the supply. That's how the sockets and lights in a house are wired.

The rules

• Voltage across every branch is the full supply voltage.
• Current splits between the branches and the branch currents add up to the total: I = I1 + I2 + I3.
• Total resistance is always less than the smallest branch resistance.
• A break in one branch only stops that branch.

Working out total resistance

1 ÷ R_T = 1 ÷ R1 + 1 ÷ R2 + 1 ÷ R3

Two shortcuts:

• Two resistors: R_T = (R1 × R2) ÷ (R1 + R2), "product over sum".
• Identical resistors: R_T = R ÷ number of resistors. Four 40 Ω in parallel is 40 ÷ 4 = 10 Ω.

Worked example

Branches of 46 Ω and 23 Ω are in parallel across 230 V.

1. Branch currents: 230 ÷ 46 = 5 A and 230 ÷ 23 = 10 A
2. Total current: 5 + 10 = 15 A
3. Total resistance: (46 × 23) ÷ (46 + 23) = 1,058 ÷ 69 = 15.33 Ω
4. Check: 230 ÷ 15.33 = 15 A

Exam tip: if your total resistance comes out bigger than the smallest branch, you've added instead of using the parallel formula.

Try it: Ohm's law calculator