Series circuits

In a series circuit everything is in one loop. The same current flows everywhere, the supply's p.d. is shared between the components, and the resistances add up. If one part breaks, the whole loop stops.

Key facts

  • Series: same current everywhere; p.d.s add up to the supply; R_total = R₁ + R₂ + …
  • In series, the bigger resistor gets the bigger share of the p.d.
  • If one bulb breaks in series, the loop is broken and all the bulbs go out.
  • Cells in series, facing the same way, add their p.d.s: two 1.5 V cells give 3 V.

Worked examples

Example 1

Three lamps are in series with a cell. The ammeter next to the cell reads 0.2 A. What do ammeters placed between the lamps read?

  1. In a series circuit there is only one path, so the same charge flows through every part.
  2. So the current is the same everywhere: every ammeter reads 0.2 A.

Answer: 0.2 A everywhere

Example 2

One bulb breaks in a series circuit of three bulbs. What happens to the other two?

  1. A series circuit has only one loop.
  2. The broken bulb leaves a gap, so no current flows anywhere and every bulb goes out.

Answer: They go out too.

Example 3

A switch is opened in a series circuit with two lamps. Which lamps go off?

  1. The switch is part of the only loop.
  2. Opening it breaks the loop, so no current flows through either lamp.

Answer: Both lamps go off.

Example 4

Two 1.5 V cells are joined in series, facing the same way. What is their total p.d.?

  1. Cells joined in series, facing the same way, add their p.d.s.
  2. Add them. 1.5 + 1.5 = 3 V

Answer: 3 V

Example 5

Two lamps are in series with a 9 V battery. The voltmeter across one lamp reads 5 V. What does the voltmeter across the other lamp read?

  1. In series, the battery's p.d. is shared between the lamps.
  2. The two readings add up to the battery's p.d. 9 − 5 = 4 V

Answer: 4 V

Example 6

A second lamp is added in series with the first. What happens to the brightness, and why?

  1. The two lamps share the battery's p.d., and the total resistance is bigger.
  2. So less current flows, and each lamp is dimmer than one lamp on its own.

Answer: Both lamps are dimmer.

Example 7

Resistors of 3 Ω, 5 Ω and 4 Ω are in series. What is the total resistance?

  1. In series, the current goes through every resistor in turn.
  2. So the resistances simply add. R = 3 + 5 + 4 = 12 Ω

Answer: 12 Ω

Example 8

A 6 V battery is connected to 10 Ω and 20 Ω resistors in series. What current flows?

  1. Add the resistances. R = 10 + 20 = 30 Ω
  2. The same current flows through both. I = 6 ÷ 30 = 0.2 A

Answer: 0.2 A

Example 9

A 12 V battery is connected to 4 Ω and 2 Ω resistors in series. Find the current and the p.d. across each resistor.

  1. Series resistances add. R = 4 + 2 = 6 Ω
  2. Use I = V ÷ R. I = 12 ÷ 6 = 2 A
  3. Use V = IR for each resistor. V₁ = 2 × 4 = 8 V, V₂ = 2 × 2 = 4 V
  4. Check: the p.d.s add up to the supply. 8 + 4 = 12 V ✓

Answer: 2 A; 8 V and 4 V

Example 10

A 12 V supply is connected across 3 kΩ and 1 kΩ resistors in series. Find the p.d. across the 3 kΩ resistor without working out the current.

  1. The p.d. is shared in the ratio of the resistances. 3 : 1
  2. The 3 kΩ resistor gets 3 parts out of 4. ¾ × 12 = 9 V

Answer: 9 V