The resistance of hot tungsten filament is about 10 times the cold resistance. What will be the resistance of 100 W and 200 V lamp when not in use?

Options

A. `14,000 Omega`
B. `400 Omega`
C. `40 Omega`
D. `4 Omega`

Explanation

To find the resistance of the 100 W and 200 V lamp when not in use, we can follow these steps:

### Step 1: Understand the relationship between hot and cold resistance
The problem states that the resistance of the hot tungsten filament (R_hot) is about 10 times the cold resistance (R_cold). This can be expressed as:
\[ R_{hot} = 10 \times R_{cold} \]

### Step 2: Calculate the hot resistance using the power formula
When the lamp is in use, we can calculate the hot resistance (R_hot) using the power formula. The power (P) of the lamp is given as 100 W, and the voltage (V) is given as 200 V. The relationship between power, voltage, and resistance is given by:
\[ P = \frac{V^2}{R} \]
Rearranging this formula to solve for resistance gives us:
\[ R = \frac{V^2}{P} \]

### Step 3: Substitute the values into the formula
Now we can substitute the given values into the formula:
\[ R_{hot} = \frac{(200 \, V)^2}{100 \, W} \]
Calculating this gives:
\[ R_{hot} = \frac{40000 \, V^2}{100 \, W} = 400 \, \Omega \]

### Step 4: Calculate the cold resistance
Using the relationship established in Step 1, we can find the cold resistance (R_cold):
\[ R_{cold} = \frac{R_{hot}}{10} = \frac{400 \, \Omega}{10} = 40 \, \Omega \]

### Conclusion
Thus, the resistance of the lamp when not in use (cold resistance) is:
\[ R_{cold} = 40 \, \Omega \]

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