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Lesson 4 of 5

Series circuits

One road, no junctions. Everything charge does, it does one after another.

One path, no choices

A series circuit is the simplest kind: every component sits on a single loop, one after another, with no junctions. Every scoop of charge that leaves the battery has to pass through every component before it gets home — there's no other route available.

Rule 1 Because there's only one path, exactly the same current flows through every component in a series circuit — including the ammeter, wherever you put it.

Voltages add up

Each resistor takes a bite out of the charge's energy as it passes through. By the time the charge gets back to the battery, all of the energy the battery gave it (its EMF) must be spent — there's nowhere else for it to go. So the p.d.s across each series component always add up to the total EMF.

V1 + V2 + … = EMF

And since the same current flows through both resistors, you can also add up resistance directly:

Rtotal = R1 + R2 + …

Worked example

A 10 V battery is connected to a 2 Ω resistor in series with a 3 Ω resistor. Find the current, and the p.d. across each resistor.

Rtotal = 2 + 3 = 5 Ω

I = V / R = 10 ÷ 5 = 2 A (this is the current everywhere in the loop)

V1 = I × R1 = 2 × 2 = 4 V  ·  V2 = I × R2 = 2 × 3 = 6 V

Check: 4 + 6 = 10 V, matching the EMF. ✓

Notice There's only one ammeter symbol drawn below, even though there are two resistors — because the current is identical everywhere in a series loop, one reading tells you all of them. Drag either resistance slider and watch both voltage labels change, but their sum always lands back on the battery push.
10.0 V 2.0 Ω drops 4.0 V 3.0 Ω drops 6.0 V A 2.0 A
10.0 V
2.0 Ω
3.0 Ω
Current (same everywhere) I = 2.0 A

Energy budget

R1 4.0 V
R2 6.0 V

4.0 V + 6.0 V = 10.0 V

Quick check

Q Three identical 2 Ω resistors are connected in series to a 6 V battery. What current flows?

Rtotal = 2 + 2 + 2 = 6 Ω

I = V / R = 6 ÷ 6 = 1 A