Series Circuits — Resistance, Current and Voltage Division

In a series circuit there is only one path for current. Every element therefore carries the same current, while the source voltage is shared between the elements in proportion to their resistance.

Equivalent resistance

R_total = R1 + R2 + … + Rn

Series resistances add directly.

With the equivalent resistance known, the current follows from Ohm’s law. Each voltage drop is then the same current multiplied by that element’s resistance.

I = V_source ÷ R_total

The current is common to every series element.

Worked example

Three resistors in series

Problem. A 12 V source feeds 10 Ω, 22 Ω and 47 Ω in series. Find the current and each voltage drop.

Solution. R_total = 10 + 22 + 47 = 79 Ω. I = 12 ÷ 79 = 0.1519 A, about 151.9 mA. V1 = 0.1519 × 10 = 1.52 V; V2 = 0.1519 × 22 = 3.34 V; V3 = 0.1519 × 47 = 7.14 V. The sum is 1.52 + 3.34 + 7.14 = 12.0 V.

Voltage division and power

The largest resistance in a series string drops the largest voltage. Power dissipated in each element is P = I² × R, so the same ranking applies to heating.

The current is identical through every series element.
The voltage drops add up to the source voltage.
The largest resistance drops the largest voltage.
One open element interrupts the whole series circuit.

Series circuits fail completely when one element opens. This is a useful diagnostic fact: a string of loads that are all dead points to a common series path, not to every load failing at once.

Key points.

Series resistances add: R_total = R1 + R2 + …
Current is the same everywhere in the loop.
Voltage divides in proportion to resistance.
An open element stops current in the entire string.

Practice

Worked example

Two 6 Ω resistors in series across 12 V give R_total = 12 Ω, I = 1 A and 6 V across each resistor.