Electrical Power, EMF, and Internal Resistance

Whenever charge moves through a potential difference, energy is transferred. Recalling that the work done in moving charge $q$ through a potential difference $V$ is $W = qV$, and that current is charge per unit time, we can find the rate of energy transfer, which is the electrical power. Combining $P = \frac{W}{t}$ with $q = It$ gives

$$P = VI$$

Power is measured in watts ($\text{W}$), where one watt is one joule per second. This equation tells us that a device carrying a large current across a large voltage transfers energy rapidly. Using Ohm's law we can write power in two other useful forms. Substituting $V = IR$ gives $P = I^2 R$, and substituting $I = \frac{V}{R}$ gives $P = \frac{V^2}{R}$. The form $P = I^2 R$ is especially important for understanding energy dissipated as heat in a r