Electrical Power Formula (P = IV)

A transmission line carrying 1,000 amps at 345,000 volts delivers 345 megawatts. The same 1,000 amps at 120 volts delivers only 120 kilowatts. Voltage makes the difference, and the relationship is direct multiplication.

P = IV: electrical power equals current times voltage. This single formula is the quantitative bridge between circuit quantities and energy delivery. Combined with Ohm's Law (V = IR), it yields two more forms: P = I²R (power dissipated as heat, critical for transmission losses) and P = V²/R (power at a given voltage across a resistance).

P = IV explains why the grid operates at high voltage. For a fixed power delivery, I = P/V. Doubling voltage halves current. Since resistive losses scale with I²R, halving current cuts losses by a factor of four. The entire voltage architecture of the grid (generators at ~20 kV, step-up to 345-765 kV for transmission, step-down to 120/240 V for homes) follows directly from this formula.

Worked Example

A Level 2 EV charger runs on a 240 V, 40 A circuit.

• Calculate maximum power. P = 240 x 40 = 9,600 W, enough to add roughly 25 miles of range per hour.

The homeowner also wants to run a 240 V, 30 A electric dryer on its own circuit at the same time as the charger, with everything else in the house drawing 60 A. Does the 200 A main panel hold?

The dryer draws 240 x 30 = 7,200 W. Combined current: 40 + 30 + 60 = 130 A, under the 200 A limit. The panel holds today, but a second EV would push it over. P = IV is why panel capacity, not just wiring, becomes the bottleneck as homes electrify.

P = IV is behind every grid voltage decision, every breaker rating, and every transmission loss calculation.

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