Potential differences add in series

The idea

The total potential difference across resistors in series equals the sum of the potential differences across the individual resistors: V = V1 + V2 + V3.

Sharing the push

A battery gives 12 V across three resistors joined in series. A voltmeter shows 2 V across the first resistor and 4 V across the second.

What will the voltmeter show across the third resistor?

• 6 V, so the three add up to the battery's 12 V
• 12 V, the same as the battery
• 2 V, the same as the first

Sharing 12 volts

Press Next step to see the potential difference across each resistor and then add them.

The parts add to the whole

The potential difference across the whole row of resistors was exactly the sum of the potential differences across the single resistors.

The total potential difference across resistors in series equals the sum of the potential differences across the individual resistors: V = V₁ + V₂ + V₃.

Notes

In series, the total potential difference equals the sum of the potential differences across the individual resistors: V = V₁ + V₂ + V₃.

Check yourself

Three resistors are in series. The potential differences across them are 2 V, 4 V and 6 V. What is the total potential difference across the combination, in V?

Answer: 12 V

V = V₁ + V₂ + V₃ = 2 V + 4 V + 6 V = 12 V.

A 9 V battery is joined across two resistors in series. The potential difference across the first is 4 V. What is it across the second, in V?

Answer: 5 V

V = V₁ + V₂ gives 9 V = 4 V + V₂, so V₂ = 5 V.

For resistors in series, how is the total potential difference related to the individual ones?

• It equals their sum — correct. Yes!
• It equals the largest of them. The total is the sum of all the individual potential differences, not just the largest.
• Each resistor has the full total across it. In series the total is shared out among the resistors. The individual potential differences add up to the total.