Series Circuits

DC Circuits · 10 min read

Old Christmas lights had a dirty secret: one bulb blew and the whole string went dark. Every bulb was wired on the same loop — one break, no lights.

Industrial machines use the same idea deliberately: a chain of emergency-stop buttons wired in series means pressing any one shuts the whole machine down immediately.

What “Series” Means

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

Every electron that leaves the battery must pass through every component in turn before returning.

The Two Golden Rules

Current

Same current flows through every component

Voltage

Individual voltage drops add up to the source voltage

Total Resistance

Series resistors simply add up. The total is always larger than any individual resistor:

R_{total} = R_{1} + R_{2} + \dots + R_{n}

Once you have $R_{total}$ , Ohm's Law gives the current: $I = V / R_{total}$ .

Voltage Drops

Because the same current flows through every resistor, the voltage dropped across each one is:

V_{i} = I \cdot R_{i}

A bigger resistor drops more voltage. The drops always sum to the source.

Worked Example

Three resistors — 2 Ω, 4 Ω, and 6 Ω — connected in series to a 12 V battery. Find the current and each voltage drop.

Find total resistance: $R_{total} = 2 + 4 + 6 = 12 \text{ Ω}$
Find current: $I = V / R_{total} = 12 / 12 = 1 \text{ A}$
Find each drop: $V_1 = 1 \times 2 = 2 \text{ V}$ , $V_2 = 1 \times 4 = 4 \text{ V}$ , $V_3 = 1 \times 6 = 6 \text{ V}$
Verify: $V_{source} = 2 + 4 + 6 = 12 \text{ V}$ ✓

Series circuits share current and split voltage. The largest resistor always drops the most voltage; the smallest drops the least.

Think Before Calculating

Predict the outcome first — then verify with the series circuit rules.

Scenario 1: Three resistors — 2 Ω, 4 Ω, 6 Ω — are in series with a 12 V source. What is the current?

Scenario 2: You double every resistor value but keep the voltage at 12 V. What happens to the current?

Scenario 3: You add a fourth 6 Ω resistor in series (source still 12 V). What happens to the existing voltage drops?

Common Mistakes

Series Circuit Playground

Drag the sliders and watch how the voltage divides. The coloured bar shows which resistor “eats” the most voltage.

Voltage12.0 V

1 V24 V

R₁2 Ω

R₂4 Ω

R₃6 Ω

R_{total} = R_1 + R_2 + R_3

12 Ω

Current (I = V / R)

1.000 A

Voltage drops across each resistor

✅ Series = single loop, one path for current
✅ Current is identical at every point in the loop
✅ Total resistance = sum of all resistors
✅ Bigger resistor → bigger voltage drop
✅ All voltage drops add up to the source voltage