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 determine how the stored energy in a capacitor changes when the charge is increased from \( Q \) to \( 2Q \).

### Step-by-Step Solution:

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

2. **Substitute the initial charge**:
For the initial condition where the charge is \( Q \), the stored energy is:
\[ W = \frac{1}{2} \frac{Q^2}{C} \]

3. **Increase the charge to \( 2Q \)**:
Now, if the charge is increased to \( 2Q \), we need to calculate the new stored energy \( W' \):
\[ W' = \frac{1}{2} \frac{(2Q)^2}{C} \]

4. **Calculate \( (2Q)^2 \)**:
Simplifying \( (2Q)^2 \):
\[ (2Q)^2 = 4Q^2 \]
Therefore, we can rewrite the expression for \( W' \):
\[ W' = \frac{1}{2} \frac{4Q^2}{C} \]

5. **Factor out the original energy**:
We can factor out the original energy \( W \) from this expression:
\[ W' = 4 \left(\frac{1}{2} \frac{Q^2}{C}\right) = 4W \]

6. **Conclusion**:
Thus, when the charge is increased to \( 2Q \), the stored energy becomes:
\[ W' = 4W \]

### Final Answer:
The stored energy will be \( 4W \).

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