Problem — resistance and power of an ohmic conductor

Problem

A voltage of $6{,}0\ \text{V}$ is applied across an ohmic conductor and a current of $0{,}50\ \text{A}$ is measured. Calculate the conductor’s resistance and the power dissipated.

Solution

Resistance from Ohm’s first law: $R = \frac{V}{i} = \frac{6{,}0\ \text{V}}{0{,}50\ \text{A}} = 12\ \Omega$

Power dissipated (Joule heating): $P = V\,i = 6{,}0\ \text{V} \cdot 0{,}50\ \text{A} = 3{,}0\ \text{W}$

Check with the equivalent forms $P = R\,i^2 = 12 \cdot 0{,}50^2 = 3{,}0\ \text{W}$ and $P = V^2/R = 36/12 = 3{,}0\ \text{W}$: they match.

$\ev{R = 12\ \Omega \qquad P = 3{,}0\ \text{W}}$

Links

Topics: Electric circuits Concepts: Ohm’s law · Power