Physics / Unit 9: Electricity and Circuits
9.7 Electric Power and Energy
Notes
Electric power is the rate at which electrical energy is used: $P = IV$.
- Using Ohm's law: $\displaystyle P = I^2R = \frac{V^2}{R}$. Unit: watts (W).
- Energy used: $E = Pt$. Utilities bill in kilowatt-hours (kWh): $1 \text{ kWh} = 1000 \text{ W} \times 3600 \text{ s} = 3.6 \times 10^6 \text{ J}$.
- Cost $=$ energy in kWh $\times$ price per kWh.
- Example: a 100 W lamp on for 5 h uses $0.1 \text{ kW} \times 5 \text{ h} = 0.5 \text{ kWh}$. At $0.20 per kWh, that costs $0.10.
Practice
A laptop charger draws 0.5 A from a 120 V outlet. What power does it use?
$P = IV = 0.5 \times 120 = 60 \text{ W}$.
A 1,500 W space heater runs for 4 hours. Electricity costs $0.15 per kWh. What is the cost?
$E = 1.5 \text{ kW} \times 4 \text{ h} = 6 \text{ kWh}$; $6 \times 0.15 = 0.90$.
A $4 \text{ } \Omega$ resistor is connected to a 12 V battery. What power does it use?
$\displaystyle P = \frac{V^2}{R} = \frac{144}{4} = 36 \text{ W}$.
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