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Series Circuits

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One path

Components are in series when current has only one path through them.

Reading the schematic: straight lines are wires; the unequal parallel lines are a cell/battery symbol; a zigzag is a resistor; a circle marked V is a voltmeter; a circle marked A is an ammeter. Labels beside the symbols tell us their values.
12 V R1 = 2 Ω R2 = 4 Ω I = 2 A everywhere

A useful first picture

What does RT mean?

R means resistance. The small subscript T means total. Therefore RT means total resistance.

You will see this same idea elsewhere: for example, IT means total current.

Think of a one-lane road with several toll booths. Every car that passes one booth must pass all the others. In a series circuit, the same current passes through every component.

What is really happening?

Charge does not pile up continuously at one resistor and disappear at another. In steady-state DC operation, the rate of charge flow is the same around the single loop. The source voltage is divided among the series components according to their electrical behavior.

A little history

Gustav Kirchhoff developed powerful circuit rules in the 1840s. One says that voltage rises and drops around a closed loop must balance. That principle explains why the voltage drops in our series example add back to the source voltage.

Worked example

12 V 2 Ω 4 Ω I = 2 A

R1 = 2 Ω and R2 = 4 Ω on a 12 V source.

RT = 2 + 4 = 6 Ω
I = 12 ÷ 6 = 2 A

R1 drop = 2 A × 2 Ω = 4 V.
R2 drop = 2 A × 4 Ω = 8 V.
4 V + 8 V = 12 V.

Try these yourself

Two resistors, 3 Ω and 5 Ω, are in series. What is total resistance? source 3 Ω 5 Ω
Series resistances add: 3 Ω + 5 Ω = 8 Ω.
In a simple series circuit, which quantity is the same through every component? source R1 R2 same I
A series circuit has one path, so the same current flows through each component.
A 12 V source has voltage drops of 4 V and 8 V in series. Their total is: 12 V 4 V drop 8 V drop
The series voltage drops add to the source voltage: 4 V + 8 V = 12 V.

A little deeper

For resistors in series:

RT = R1 + R2 + R3 + ...

The same current flows through each resistor, but the voltage drop across each resistor depends on its resistance.

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