Question

An electric fan and a heater are marked 100W, 220V and 1000W, 220V respectively. The resistance of the heater is ____ .

• A. Zero
• B. Greater than that of fan
• C. Less than that of fan
• D. Equal to that of fan

Hint:

To find the resistance of an electrical device, use the formula \( R = \frac{V^2}{P} \), where \(V\) is the voltage and \(P\) is the power.

Answer 1

The Correct Option is C

We are given the power rating and voltage for both the fan and the heater. To find the resistance, we use the formula:
\[ P = \frac{V^2}{R} \] Where: - \( P \) is the power in watts,
- \( V \) is the voltage in volts,
- \( R \) is the resistance in ohms.
For the fan: \[ P_{\text{fan}} = 100 \, \text{W}, \quad V_{\text{fan}} = 220 \, \text{V} \] Substitute these values into the formula: \[ R_{\text{fan}} = \frac{V_{\text{fan}}^2}{P_{\text{fan}}} = \frac{220^2}{100} = \frac{48400}{100} = 484 \, \Omega \] For the heater: \[ P_{\text{heater}} = 1000 \, \text{W}, \quad V_{\text{heater}} = 220 \, \text{V} \] Substitute these values into the formula: \[ R_{\text{heater}} = \frac{V_{\text{heater}}^2}{P_{\text{heater}}} = \frac{220^2}{1000} = \frac{48400}{1000} = 48.4 \, \Omega \] Thus, the resistance of the heater is \( 48.4 \, \Omega \), which is less than the resistance of the fan (\( 484 \, \Omega \)).