A `100 W 200 V` bulb is connected to a `160 V` power supply. The power consumption would be

Options

A. `125 W`
B. `100 W`
C. `80 W`
D. `64 W`

Answer

To solve the problem of determining the power consumption of a `100 W`, `200 V` bulb when connected to a `160 V` power supply, we can follow these steps:

### Step 1: Determine the resistance of the bulb
The power rating of the bulb is given as `100 W` at a voltage of `200 V`. We can use the formula for power:

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

Rearranging this formula to find the resistance \( R \):

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

Substituting the values:

\[ R = \frac{(200 \, V)^2}{100 \, W} = \frac{40000 \, V^2}{100 \, W} = 400 \, \Omega \]

### Step 2: Calculate the power consumption at `160 V`
Now that we have the resistance of the bulb, we can calculate the power consumption when the bulb is connected to a `160 V` power supply using the same power formula:

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

Substituting the new voltage and the resistance we found:

\[ P = \frac{(160 \, V)^2}{400 \, \Omega} \]

Calculating this gives:

\[ P = \frac{25600 \, V^2}{400 \, \Omega} = 64 \, W \]

### Conclusion
The power consumption of the `100 W`, `200 V` bulb when connected to a `160 V` power supply is **64 W**.

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