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 finding 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: Calculate the Resistance of the Bulb
We know that the power \( P \) of an electrical device can be expressed in terms of voltage \( V \) and resistance \( R \) using the formula:
\[ P = \frac{V^2}{R} \]
From this, we can rearrange the formula to find the resistance \( R \):
\[ R = \frac{V^2}{P} \]
Substituting the values for the bulb (where \( V = 200 \, V \) and \( P = 100 \, W \)):
\[ R = \frac{200^2}{100} \]
Calculating this gives:
\[ R = \frac{40000}{100} = 400 \, \Omega \]

### Step 2: Calculate the Power Consumption at 160 V
Now that we have the resistance, we can find the new power consumption when the bulb is connected to a 160 V power supply. Using the power formula again:
\[ P_1 = \frac{V_1^2}{R} \]
Where \( V_1 = 160 \, V \) and \( R = 400 \, \Omega \):
\[ P_1 = \frac{160^2}{400} \]
Calculating this gives:
\[ P_1 = \frac{25600}{400} = 64 \, W \]

### Final Answer
The power consumption of the bulb when connected to a 160 V power supply is \( 64 \, W \).

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