Electrical Power and Energy Calculations

Electrical power is the rate at which energy is transferred by an electrical component.

Power equations

$P = IV$

Combining with $V = IR$ gives two additional forms:

$P = I^2R \qquad P = \frac{V^2}{R}$

Symbol	Quantity	Unit
$P$	Power	W
$I$	Current	A
$V$	Potential difference	V
$R$	Resistance	$\Omega$

Energy transferred

$E = Pt = IVt$

Symbol	Quantity	Unit
$E$	Energy transferred	J
$t$	Time	s

Worked example: power

A 230 V kettle draws a current of 10 A. Calculate the power.

$P = IV = 10 \times 230 = 2300\text{ W} = 2.3\text{ kW}$

Worked example: energy

The kettle runs for 3.0 minutes. Calculate the energy transferred.

$t = 3.0 \times 60 = 180\text{ s}$

$E = Pt = 2300 \times 180 = 414\,000\text{ J} = 414\text{ kJ}$

Choosing the right equation

Known values	Use
$I$ and $V$	$P = IV$
$I$ and $R$	$P = I^2R$
$V$ and $R$	$P = V^2/R$

Common errors and how to correct them

Using the wrong power equation. Choose based on which two quantities you know. If you have $V$ and $R$ but not $I$, use $P = V^2/R$ directly rather than finding $I$ first (though both methods work).

Forgetting to square the current in $P = I^2R$. The $I$ is squared, not just multiplied. $P = I^2R$ is not the same as $P = IR$.

How to apply this in an exam

Write the equation you are using, substitute, and calculate. Convert time to seconds for energy calculations. State the unit (W for power, J for energy).