Resistance in series
Resistors in series add: Rs = R₁ + R₂ + R₃. A 20 Ω and a 4 Ω resistor in series make 24 Ω, so a 6 V cell drives 6 / 24 = 0.25 A through both.
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Equivalent resistance24 Ωbetween A and B
Current0.25 Afrom the cell
Power1.5 WP = VI
| R | I | V | Power | |
|---|---|---|---|---|
| R₁ | 20 Ω | 0.25 A | 5 V | 1.25 W |
| R₂ | 4 Ω | 0.25 A | 1 V | 0.25 W |
Step by step
- All in series: Req = 20 + 4 = 24 Ω
- Current from the cell: I = V / Req = 6 / 24 = 0.25 A
- Drops in series: R₁: 0.25 × 20 = 5 V, R₂: 0.25 × 4 = 1 V.
- Power: P = EI = 6 × 0.25 = 1.5 W.
Why it works
- In series the same current I flows through every resistor, because there is only one path.
- By Ohm's law the voltage across each one is V₁ = IR₁, V₂ = IR₂ and V₃ = IR₃.
- The cell's voltage is shared between them: V = V₁ + V₂ + V₃.
- So IRs = IR₁ + IR₂ + IR₃, and cancelling I gives Rs = R₁ + R₂ + R₃.
- Rs is always larger than the largest resistor in the chain.
Resistance in series: quick answers
What is the formula for resistance in series?
Rs = R₁ + R₂ + R₃ + ... The same current flows through each resistor and the voltages across them add up to the supply voltage.
What current flows through 20 Ω and 4 Ω in series on 6 V?
Rs = 24 Ω, so I = 6 / 24 = 0.25 A. The 20 Ω resistor drops 5 V and the 4 Ω resistor 1 V.
What happens if one resistor in a series circuit breaks?
The only path is broken, so the current stops everywhere. That is why the appliances in a house are joined in parallel, not in series.