A lamp is marked 60 W, 220 V. If it operates at 200 V, the rate of consumption of energy will

Options

A. decrease
B. increase
C. remain unchanged
D. first increase then decrease

Explanation

To solve the problem, we need to determine the rate of energy consumption (power) of a lamp when it operates at a voltage different from its rated voltage. The lamp is rated at 60 W when operating at 220 V.

### Step-by-Step Solution:

1. **Understand the Power Formula**:
The power (P) consumed by an electrical device can be expressed using the formula:
\[ P = \frac{V^2}{R} \]
where \( V \) is the voltage and \( R \) is the resistance.

2. **Calculate the Resistance of the Lamp**:
When the lamp operates at its rated voltage of 220 V and consumes 60 W, we can rearrange the power formula to find the resistance \( R \):
\[ R = \frac{V^2}{P} \]
Substituting the values:
\[ R = \frac{220^2}{60} \]
Calculate \( R \):
\[ R = \frac{48400}{60} \approx 806.67 \, \Omega \]

3. **Calculate Power at 200 V**:
Now, we will find the power consumption when the lamp operates at 200 V. Using the power formula again:
\[ P_2 = \frac{V_2^2}{R} \]
Substituting \( V_2 = 200 \, V \) and the resistance \( R \) we calculated:
\[ P_2 = \frac{200^2}{806.67} \]
Calculate \( P_2 \):
\[ P_2 = \frac{40000}{806.67} \approx 49.5 \, W \]

4. **Conclusion**:
The rate of consumption of energy when the lamp operates at 200 V is approximately 49.5 W. This is less than the rated power of 60 W at 220 V.

### Final Answer:
The rate of consumption of energy will be approximately **49.5 W** when the lamp operates at 200 V.

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