Electricity and magnetism

Electrical work and power

Current transfers electrical energy into other forms. Power is the rate of energy transfer; for a DC circuit, $P=UI$ .

As charge passes through a circuit element with a potential difference, the electric field does work. That energy may heat a resistor, produce light, or turn a motor. In an ideal circuit model, electrical energy transferred equals the work done by the electric force.

W=UQ=UIt,\qquad P=\frac{W}{t}=UI\quad(\text{DC}),\qquad W=Pt

Definition: Electrical work and power

Work $W$ is measured in joules (J) and power $P$ in watts (W). Here $U$ is voltage, $I$ current, and $t$ time. For an ohmic resistor, Ohm’s law gives equivalent forms $P=I^2R=U^2/R$ .

Adjust voltage, current, and time to track power and electrical energy transferred to a load.

Electrical energy and energy use

At constant power, a device uses more energy the longer it operates: $W=Pt$ . Electricity bills commonly use the kilowatt-hour: $1\,\mathrm{kWh}=3.6\times10^6$ J. A kWh is a unit of energy, not power.

Example: A lamp operating for one hour

A $60$ W lamp operates at its rated conditions for $1.0$ hour. Find the energy used in J and kWh.

Solution

$W=Pt=60\times3600=216000$ J. In kWh, $0.060$ kW $\times1.0$ h $=0.060$ kWh.

For a pure resistor, instantaneous power is $p=ui$ ; when voltage and current are constant, $P=UI$ . Heat released over time $t$ follows Joule–Lenz law, $Q=I^2Rt$ . For example, a $10\,\Omega$ resistor carrying $0.50$ A dissipates $2.5$ W; in $4$ minutes it converts $600$ J into heat. Check the time unit before converting energy to joules.

A device’s rated power applies at its specified voltage. Using the wrong voltage can make it underperform or overheat; power equations do not replace following the manufacturer’s safety ratings.

Quick check

How much energy does a 100 W device use in 10 s?

Which is a unit of electrical energy commonly shown on a utility bill?

References

Young, Freedman (2019). University Physics