Series Circuit

In a series circuit all components are connected end-to-end in a single loop. The same current flows through every component, but voltages add up.

What Is a Series Circuit?

In a series circuit, all components are wired in a single loop. There is only one path for current to flow.

Battery and two resistors connected in a single loop — a series circuit.

Key Rules

Total Resistance — Series

R_{total} = R_1 + R_2 + R_3 + \ldots

Resistances simply add up in a series circuit.

Current — Series

I_1 = I_2 = I_3 = I

The same current flows through every component.

Voltage — Series

V_{total} = V_1 + V_2 + V_3 + \ldots

Voltages across components add up to the supply voltage.

Ohm's Law

$V = I \times R$

Where $V$ is voltage (volts, V), $I$ is current (amperes, A), $R$ is resistance (ohms, Ω).

Warning If one component in a series circuit breaks (opens), the entire circuit stops working — like old-style Christmas lights.

Two resistors R₁ = 4 Ω and R₂ = 6 Ω are in series with a 10 V battery. Find the current.

$R_{total} = 4 + 6 = 10\,\Omega$

$I = \frac{V}{R} = \frac{10}{10} = 1 \text{ A}$

Real world: Battery-powered torch (flashlight)

A simple torch is a series circuit: batteries, switch, and bulb all in one loop. The total resistance of the circuit equals the bulb resistance plus any internal resistance of the batteries. When the switch opens the loop, current stops and the bulb goes out.

Real world: Decorative LED fairy lights (old style)

Traditional string Christmas lights were wired in series — if one bulb's filament burned out, it broke the single current path and the entire string went dark. Modern fairy lights use parallel wiring (or self-shunting bulbs) to avoid this problem.

Real world: Volume control with a rheostat

A variable resistor (rheostat) wired in series with a speaker controls volume. Increasing the resistance increases the total series resistance, reducing the current through the speaker coil — so the speaker produces a quieter sound. Turning the knob decreases resistance, allowing more current and louder audio.

Tip Where do you see series circuits in real life? Torches, simple battery-powered toys, some festive string lights, and basic on/off switches are all classic series circuit applications!

Practice Problems

Three resistors of 2 Ω, 3 Ω, and 5 Ω are in series. What is the total resistance?

Show answer

R_total = 2 + 3 + 5 = 10 Ω.

A 12 V battery drives a current of 2 A through a series circuit. What is the total resistance?

Show answer

R = V/I = 12/2 = 6 Ω.