Power and Resistance Calculator (P = I²R)

GCSE PhysicsAQAEdexcelOCRFoundation & Higher

Find power, current or resistance using P = I² × R. The working shows the squaring step, and the square root when you are finding current.

Quick answer

Power = current² × resistance. Square the current in amps, then multiply by the resistance in ohms to get watts. For example, 2 A through 15 Ω gives P = 2² × 15 = 60 W. To find current, use I = √(P ÷ R).

By Mehmood Kakar · Updated

P = I² × R
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How to use P = I²R

When current flows through a resistor, energy is transferred and the resistor heats up. The power depends on the current and the resistance:

power = (current)² × resistance

  • P is power in watts (W)
  • I is current in amperes (A)
  • R is resistance in ohms (Ω)

A current of 2 A through a 15 Ω resistor gives P = 2² × 15 = 4 × 15 = 60 W. Square the current first, then multiply.

Because the current is squared, doubling it makes the power four times bigger. That is why the National Grid transmits electricity at a very high potential difference: for the same power, a high p.d. means a small current, and a small current wastes far less energy heating the cables.

To find current, divide power by resistance and then take the square root. Forgetting that last step is the most common mistake on this equation.

Common mistakes that cost marks

  1. Not squaring the current. 2 A × 15 Ω = 30 is wrong; 2² × 15 = 60 W is right.
  2. Forgetting the square root. When finding current, P ÷ R gives I², not I.
  3. Squaring before converting. Convert mA to A first: 200 mA = 0.2 A, and 0.2² = 0.04.
  4. Calculator order. Typing 2 × 15² squares the resistance instead. Square only the current.

Practice questions

Try each one on paper first, then reveal the worked answer.

Q1A current of 2.0 A flows through a 15 Ω resistor. Calculate the power transferred.[2 marks]
  1. P = I² × R
  2. P = 2.0² × 15 = 4.0 × 15
  3. P = 60 W
Q2A heating element transfers 36 W when the current is 3.0 A. Calculate its resistance.[3 marks]
  1. Rearrange: R = P ÷ I²
  2. I² = 3.0² = 9.0
  3. R = 36 ÷ 9.0
  4. R = 4.0 Ω
Q3A 25 Ω resistor transfers 100 W. Calculate the current through it.[3 marks]
  1. Rearrange: I = √(P ÷ R)
  2. P ÷ R = 100 ÷ 25 = 4.0
  3. I = √4.0
  4. I = 2.0 A

Frequently asked questions

What is P = I²R used for?

It gives the power transferred in a component when you know the current through it and its resistance. Power is in watts (W), current in amps (A) and resistance in ohms (Ω).

How is P = I²R related to P = VI?

Substitute V = IR into P = VI and you get P = I × R × I = I²R. Both equations give the same answer.

How do I find current from P = I²R?

Divide power by resistance to get I², then take the square root: I = √(P ÷ R).

Why does the National Grid use a high potential difference?

For the same power, a higher potential difference means a lower current. Since P = I²R, a lower current wastes much less energy heating the transmission cables.