← Electrical power

Pick the right power formula

Three formulas now give power: P = IV, P = V²/R, and P = I²R. A problem hands you two quantities. The skill is reading which two you have, and reaching for the formula that uses exactly those two.

Here is one resistor on a test bench, with three versions of the same problem.

Version 1 gives the current through the resistor and the voltage across it. P = IV uses exactly those two. So P = IV finds the power directly.

But version 2 gives the current through the resistor and its resistance. P = IV needs the voltage, which is not given. P = I²R uses exactly those two. So P = I²R finds the power directly.

And version 3 gives the voltage across the resistor and its resistance. P = V²/R uses exactly those two. So P = V²/R finds the power directly.

'Directly' means one formula, one substitution. With the voltage and the resistance, P = IV could still get there, but only after I = V/R finds the current first. Two steps instead of one.

Match the formula to the pair you are given: current and voltage take P = IV; current and resistance take P = I²R; voltage and resistance take P = V²/R.
You are givenReach forthe current and the voltageP = IV
Version 1's given pair fills the first row.
You are givenReach forthe current and the voltageP = IVthe current and the resistanceP = I²R
Version 2 adds a second row for its different given pair.
You are givenReach forthe current and the voltageP = IVthe current and the resistanceP = I²Rthe voltage and the resistanceP = V²/R
Version 3 completes the table: three given pairs, each matched to the formula that uses exactly those two.

A 30 Ω resistor carries 2.0 A. Which formula gives its power directly?

A 12 Ω resistor has 18 V across it. Which formula gives its power directly?

A charger supplies 1.5 A at 5.0 V. Which formula gives its power directly?

Name the given pair first; the formula follows.

A 60 Ω element has 120 V across it. Which formula gives its power directly?

A wire of 0.5 Ω carries 12 A. Which formula gives its power directly?

A motor draws 6.0 A at 24 V. Which formula gives its power directly?

Your turn

Only a resistor's current and its resistance are known. Which formula gives its power directly?

Only the voltage across a heater element and its resistance are known. Which formula gives its power directly?

A battery drives 0.75 A through a lamp with 9.0 V across it. Which formula gives the lamp's power directly?