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: Power Formula
Power (\( P \)) consumed is calculated as:
\[P = I^2 R\]Where \( I \) is current and \( R \) is resistance.

Step 2: Power Calculation
Given \( I = 5 \, \text{A} \) and \( R = 10 \, \Omega \).
\[P = (5)^2 \times 10 = 25 \times 10 = 250 \, \text{W}\]The heater's power is \( 250 \, \text{W} \) or \( 0.25 \, \text{kW} \).

Step 3: Energy Consumption Formula
Energy (\( E \)) consumed is calculated as:
\[E = P \times t\]Where \( t \) is time in hours and \( P \) is power in kilowatts.

Step 4: Energy Consumption Calculation
For \( t = 2 \, \text{hours} \) and \( P = 0.25 \, \text{kW} \):
\[E = 0.25 \times 2 = 0.5 \, \text{kWh}\]The heater consumed \( 0.5 \, \text{kWh} \) of energy.

Final Results:
- Heater Power: \( 250 \, \text{W} \) or \( 0.25 \, \text{kW} \).
- Energy Consumed: \( 0.5 \, \text{kWh} \).