Power: P = I² R

The idea

This is the symbolic form of the power equation linking power P in watts, current I in amperes and resistance R in ohms. It applies to any component obeying Ohm's law and describes the rate at which electrical energy is transferred to thermal energy in a resistor. Because current is squared, the equation shows that increasing current has a much larger effect on power than increasing resistance. For example, if I = 2 A and R = 5 Ω, then P = 2² × 5 = 4 × 5 = 20 W. The equation can be rearranged as I = √(P ÷ R) and R = P ÷ I². It is consistent with P = VI and V = IR, since substituting V = IR into P = VI gives P = I²R. Use SI units throughout and remember that the square applies only to the current.

What earns the marks

• Identify each symbol: P is power in watts, I is current in amperes and R is resistance in ohms.
• Substitute numerical values into P = I² R, square the current and multiply by resistance.
• Rearrange the equation to make current or resistance the subject, for example I = √(P ÷ R).
• Show that P = I² R follows from combining P = VI with V = IR.
• Use the equation to compare power dissipation in components with different currents or resistances.

Common mistakes and how to put them right

• Squaring the whole product IR instead of only the current.

  Put it right: Apply the square to I only, so P = I² × R.

• Forgetting to take the square root when rearranging for current.

  Put it right: I = √(P ÷ R), not P ÷ R.

• Mixing units, such as using mA with Ω and expecting W.

  Put it right: Convert current to A before calculating.

Exam tips

• Quote the equation in symbol form, then substitute values clearly before evaluating.
• Check whether the question asks for power, current or resistance and rearrange before substituting.
• Use the equation to justify why high-current circuits need thicker wires to limit heating.