B.5.6—Potential difference and electrical energy transfer

Energy over time

For a steady direct current,

$$E=Pt=IVt$$

where E is electrical energy transferred in time t.

Build the relation

Potential difference is energy per charge, $$V=E/q$$, and current is charge per time, $$I=q/t$$. Combining them gives $$E=VIt$$.

Units and billing

Use seconds for t to obtain joules. Electricity billing may use kWh: $$1\,\mathrm{kWh}=3.6\times10^6\,\mathrm J$$.

Worked example from the mapped local textbook

A resistor carries $3\,\mathrm A$ with a potential difference of $6\,\mathrm V$. In one second, $3\,\mathrm C$ passes and each coulomb transfers $6\,\mathrm J$.

$$E=VIt=(6)(3)(1)=18\,\mathrm J$$

Therefore $P=E/t=18\,\mathrm W$: the resistor transfers $18\,\mathrm J$ each second.

Common trap

Do not use power in place of energy. Power is the rate of transfer; multiply by time for total energy.