Series: one path, the resistances add

In a series circuit the current has one path, so the resistances simply add and the same current flows through each part.

Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.

What it is for

A heater on the end of a long thin cable, a loose connection in a junction box, a string of the old kind of lights: every one is a series circuit, and the total is the only number the source ever sees. Miss one part of the loop and the current you calculate is wrong everywhere.

How to think about it

Add the resistances first. Then use Ohm's law once, on the total, for the current. That current is the same everywhere in the loop, so the volts across any one part are that current times that part.

Worked example

R = 3 + 5 + 12 = 20 Ω

Three resistors in a line. The total is the sum.

I = 40 V / 20 Ω = 2 A

A 40 V source across the total. One current, everywhere in the loop.

V across the 12 Ω = 2 A × 12 Ω = 24 V

Each part takes its share of the volts in proportion to its resistance.

V across the 3 Ω = 6 V, across the 5 Ω = 10 V; 6 + 10 + 24 = 40 V

The shares add back to the source. That sum is the check.

Your turn

Three resistors, 5 Ω, 10 Ω and 15 Ω, in series. Write the total.

R = 5 + 10 +

The trap

Using the source voltage across one part. The source voltage is shared out; only the total sees all of it.

Practise series circuits on HoneA question on it now, a coding challenge where there is one, and it is remembered for review. Free, no email needed.