Formulas/physics/Current Electricity/Electric Power

Electric Power

Rate of energy dissipation in a resistor. Three equivalent forms. SI unit: watt (W). For a source of EMF: P_delivered = εI, P_internal = I²r, P_external = I²R.

Class 11Class 12

Derivation

Work done by the electric field moving charge $dQ$ through potential difference $V$ :

dW = V\, dQ

Power = rate of energy transfer:

P = \frac{dW}{dt} = V\frac{dQ}{dt} = VI

Using Ohm's law $V = IR$ to substitute:

P = VI = (IR)I = I^2R

P = VI = V\cdot\frac{V}{R} = \frac{V^2}{R}

\boxed{P = VI = I^2R = \frac{V^2}{R}}

Which form to use

$P = VI$ : general — use when both $V$ and $I$ are known
$P = I^2R$ : use when current is known (series circuits — same $I$ , different $R$ )
$P = V^2/R$ : use when voltage is known (parallel circuits — same $V$ , different $R$ )

Power in a source

For a cell of EMF $\mathcal{E}$ and internal resistance $r$ delivering current $I$ :

Total power generated: $P_{total} = \mathcal{E}I$
Power lost internally: $P_{internal} = I^2r$
Power delivered to external circuit: $P_{ext} = I^2R = \mathcal{E}I - I^2r$

Remember

In a parallel circuit, the appliance with the lower resistance consumes more power ($P = V^2/R$). In a series circuit, the higher resistance consumes more power ($P = I^2R$).

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