Electrical Power
Year 9 ⚡ Electricity & Magnetism Calculate electrical power: P = VI and P = I²R.
⚡ Electrical Power
Power is the rate of energy transfer. In electrical circuits, power depends on the current flowing and the voltage across the component.
⚡ Electrical Power
$$P = IV$$
$P$ = power (W) · $I$ = current (A) · $V$ = voltage (V)
💡 Example: A toaster uses 230 V and 4 A.
P = 4 × 230 = 920 W (nearly 1 kW!)
P = 4 × 230 = 920 W (nearly 1 kW!)
📱 Phone charger: 5 V at 2 A → P = 5 × 2 = 10 W
📐 Power, Resistance, and Current
By combining P = IV with Ohm's Law (V = IR), we get two more useful power formulae.
📐 Power Formulae
$$P = I^2 R \qquad P = \frac{V^2}{R}$$🔥 Electric heater: R = 25 Ω, I = 4 A. Power = I²R = 16 × 25 = 400 W
💡 Bulb from voltage: V = 12 V, R = 48 Ω. Power = V²/R = 144/48 = 3 W
Power cables get hot because of P = I²R. Thicker wires have lower resistance → less power wasted as heat. That's why high-voltage transmission lines can use thinner cables!
💰 Electricity Costs
Electricity companies charge you for energy in kilowatt-hours (kWh), not Joules.
💰 Energy Cost
$$E\text{(kWh)} = P\text{(kW)} \times t\text{(hours)} \qquad \text{Cost} = E\text{(kWh)} \times \text{price per unit}$$🏠 Example: A 2000 W (2 kW) electric heater runs for 3 hours. At 28p per kWh:
Energy = 2 × 3 = 6 kWh. Cost = 6 × 28p = £1.68
Energy = 2 × 3 = 6 kWh. Cost = 6 × 28p = £1.68
1 kWh = 1000 W × 3600 s = 3,600,000 J = 3.6 MJ. That's the energy in your electricity "unit"!
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⚡ Electrical Power & Cost Calculator