A capacitor of capacity C hasd charge Q and stored energy is W. if the charge is increased to 2Q, then the stored energy will be

Options

A. 2W
B. W/2
C. 4W
D. W/4

Answer

To solve the problem, we need to understand the relationship between the charge (Q), capacitance (C), and stored energy (W) in a capacitor.

### Step-by-Step Solution:

1. **Understanding the Formula for Energy Stored in a Capacitor**:
The energy (W) stored in a capacitor can be expressed using the formula:
\[ W = \frac{Q^2}{2C} \]
where \(Q\) is the charge on the capacitor and \(C\) is the capacitance.

2. **Initial Conditions**:
Given that the initial charge on the capacitor is \(Q\), we can write the initial energy stored as:
\[ W = \frac{Q^2}{2C} \]

3. **Increasing the Charge**:
Now, the problem states that the charge is increased to \(2Q\). We need to find the new stored energy \(W'\) when the charge is \(2Q\).

4. **Calculating New Energy**:
Using the same formula for energy with the new charge \(2Q\):
\[ W' = \frac{(2Q)^2}{2C} \]
Simplifying this:
\[ W' = \frac{4Q^2}{2C} = \frac{2Q^2}{C} \]

5. **Relating New Energy to Initial Energy**:
From our initial energy expression \(W = \frac{Q^2}{2C}\), we can express \(W'\) in terms of \(W\):
\[ W' = 4 \left(\frac{Q^2}{2C}\right) = 4W \]

6. **Conclusion**:
Therefore, if the charge is increased to \(2Q\), the new stored energy will be:
\[ W' = 4W \]

### Final Answer:
The stored energy when the charge is increased to \(2Q\) will be \(4W\).

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