Question

An electrical heater of resistance 10 Ω draws a steady current of 5 A from the service mains for 2 hours. Find the power of this heater and the amount of energy consumed by the heater in kilowatt-hour.

Answer 1

Step 1: Formula for power
The power \( P \) consumed by an electrical appliance is given by the formula:
\[ P = I^2 R \] where \( I \) is the current and \( R \) is the resistance.

Step 2: Calculate the power
Substitute the given values: \( I = 5 \, \text{A} \) and \( R = 10 \, \Omega \).
\[ P = (5)^2 \times 10 = 25 \times 10 = 250 \, \text{W} \] So, the power of the heater is \( 250 \, \text{W} \) or \( 0.25 \, \text{kW} \).

Step 3: Formula for energy consumption
The energy \( E \) consumed by an appliance is given by the formula:
\[ E = P \times t \] where \( t \) is the time in hours and \( P \) is the power in kilowatts.

Step 4: Calculate the energy consumed
The heater runs for \( t = 2 \, \text{hours} \), and the power is \( P = 0.25 \, \text{kW} \).
\[ E = 0.25 \times 2 = 0.5 \, \text{kWh} \] So, the energy consumed by the heater is \( 0.5 \, \text{kWh} \).

Final Answer:
- The power of the heater is \( 250 \, \text{W} \) or \( 0.25 \, \text{kW} \).
- The energy consumed by the heater is \( 0.5 \, \text{kWh} \).