Assertion : Two 60 W bulbs are first connected in series and then in parallel with same battery. Total power produced in second case will become four times. Rated voltage is same for two bulbs.
Reason : In series total power produced will be 30 W and in parallel 120 W.

Options

A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true and Reason is not correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Answer

To solve the problem, we need to analyze the power consumed by two 60 W bulbs when connected in series and in parallel with the same battery.

### Step 1: Understanding the Power Ratings
Each bulb is rated at 60 W. This means that when connected to their rated voltage (let's assume it is V), each bulb consumes 60 W of power.

### Step 2: Calculate the Resistance of Each Bulb
Using the power formula:
\[ P = \frac{V^2}{R} \]
For each bulb:
\[ R = \frac{V^2}{P} = \frac{V^2}{60} \]

### Step 3: Series Connection
When the two bulbs are connected in series, the total resistance \( R_{total} \) is:
\[ R_{total} = R_1 + R_2 = R + R = 2R \]
The total power \( P_{series} \) can be calculated using:
\[ P_{series} = \frac{V^2}{R_{total}} = \frac{V^2}{2R} \]
Substituting for \( R \):
\[ P_{series} = \frac{V^2}{2 \cdot \frac{V^2}{60}} = \frac{60}{2} = 30 \text{ W} \]

### Step 4: Parallel Connection
When the two bulbs are connected in parallel, the effective resistance \( R_{effective} \) is given by:
\[ \frac{1}{R_{effective}} = \frac{1}{R} + \frac{1}{R} = \frac{2}{R} \implies R_{effective} = \frac{R}{2} \]
The total power \( P_{parallel} \) can be calculated using:
\[ P_{parallel} = \frac{V^2}{R_{effective}} = \frac{V^2}{\frac{R}{2}} = \frac{2V^2}{R} \]
Substituting for \( R \):
\[ P_{parallel} = 2 \cdot \frac{V^2}{\frac{V^2}{60}} = 2 \cdot 60 = 120 \text{ W} \]

### Step 5: Conclusion
- Total power in series: \( P_{series} = 30 \text{ W} \)
- Total power in parallel: \( P_{parallel} = 120 \text{ W} \)

Thus, the assertion that the total power produced in the second case (parallel) will become four times that of the first case (series) is correct, as \( 120 \text{ W} = 4 \times 30 \text{ W} \).

### Final Answer
Both the assertion and reason are true, and the reason correctly explains the assertion.

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