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

Options

A. 64 W
B. 80 W
C. 100 W
D. 150 W

Explanation

To solve the problem of finding the power consumption of a 100 W, 200 V bulb connected to a 160 V supply, we will follow these steps:

### Step 1: Calculate 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 given values:

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

### Step 2: Calculate the current flowing through the bulb when connected to a 160 V supply
Using Ohm's law, we can find the current \( I \) flowing through the bulb when connected to the 160 V supply:

\[ I = \frac{V}{R} \]

Substituting the values:

\[ I = \frac{160}{400} = 0.4 \, \text{A} \]

### Step 3: Calculate the power consumption of the bulb at the 160 V supply
Now we can calculate the power consumption \( P' \) when the bulb is connected to the 160 V supply using the formula:

\[ P' = V \times I \]

Substituting the values:

\[ P' = 160 \times 0.4 = 64 \, \text{W} \]

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

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