A heater of 1 kW and a tungsten bulb of 100 W both marked for 220 V.
Which of the two has greater resistance?

Options

A. Both are same
B. `R_b`
C. `R_h`
D. None of these

Explanation

To determine which of the two devices, the heater or the tungsten bulb, has greater resistance, we can use the formula for resistance based on power and voltage:

\[ R = \frac{V^2}{P} \]

where:
- \( R \) is the resistance,
- \( V \) is the voltage,
- \( P \) is the power.

### Step 1: Calculate the Resistance of the Tungsten Bulb
Given:
- Power of the bulb, \( P_b = 100 \, \text{W} \)
- Voltage, \( V = 220 \, \text{V} \)

Using the formula:
\[ R_b = \frac{V^2}{P_b} \]
\[ R_b = \frac{220^2}{100} \]
\[ R_b = \frac{48400}{100} \]
\[ R_b = 484 \, \Omega \]

### Step 2: Calculate the Resistance of the Heater
Given:
- Power of the heater, \( P_h = 1000 \, \text{W} \)
- Voltage, \( V = 220 \, \text{V} \)

Using the formula:
\[ R_h = \frac{V^2}{P_h} \]
\[ R_h = \frac{220^2}{1000} \]
\[ R_h = \frac{48400}{1000} \]
\[ R_h = 48.4 \, \Omega \]

### Step 3: Compare the Resistances
Now we compare the two resistances:
- Resistance of the bulb, \( R_b = 484 \, \Omega \)
- Resistance of the heater, \( R_h = 48.4 \, \Omega \)

Since \( R_b > R_h \), we conclude that the tungsten bulb has a greater resistance than the heater.

### Final Conclusion
The tungsten bulb has greater resistance than the heater.

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