Connecting in parallel

The second way of joining resistors gives the current a choice, and almost everything about it is the opposite of the series case.

A parallel arrangement

Connecting resistors so that the total current of the circuit divides between them is called connecting them in parallel.

Figure to be added

Figure 19.30 — three resistors R1, R2 and R3 connected in parallel, each on its own branch between the same two points, with the main current I splitting into I1, I2 and I3 and joining again.

The current divides

Here the current flowing through the circuit divides into parts and flows through each resistor. Since the sum of the currents through the individual resistors is equal to the total current flowing in the circuit:

I = I₁ + I₂ + I₃

And the voltage does not

The other half of the story matters just as much. Every branch is joined between the same two points, so every branch has the same potential difference across it — and that is what lets you work out each branch current separately.

Series

The current is the same everywhere; the potential differences add up.

Parallel

The potential difference is the same across each branch; the currents add up.

Parallel swaps what stays the same

In series, the current is shared and the voltage divides. In parallel, the voltage is shared and the current divides. Getting these the right way round is most of what network problems test.