If there are n capacitors in parallel connected to V volt source, then the energy stored is equal to

Options

A. `nCV^(2)`
B. `(1)/(2)nCV^(2)`
C. `(CV^(2))/(n)`
D. `(1)/(2n)CV^(2)`

Answer

To solve the problem of finding the energy stored in n capacitors connected in parallel to a V volt source, we can follow these steps:

### Step-by-Step Solution

1. **Understanding Capacitors in Parallel**:
- When capacitors are connected in parallel, the total or equivalent capacitance (C_eq) is the sum of the individual capacitances. If each capacitor has a capacitance of C, then for n capacitors in parallel, the equivalent capacitance is:
\[ C_{eq} = nC \]

2. **Using the Energy Formula**:
- The energy (U) stored in a capacitor is given by the formula:
\[ U = \frac{1}{2} C V^2 \]
- Here, C is the capacitance and V is the voltage across the capacitor.

3. **Substituting C_eq into the Energy Formula**:
- Since we have already determined that the equivalent capacitance for n capacitors in parallel is \( nC \), we can substitute this into the energy formula:
\[ U = \frac{1}{2} (nC) V^2 \]

4. **Final Expression for Energy**:
- Simplifying the above expression gives us the total energy stored in the system of n capacitors connected in parallel:
\[ U = \frac{1}{2} nC V^2 \]

### Conclusion
Thus, the energy stored in n capacitors connected in parallel to a V volt source is:
\[ U = \frac{1}{2} nC V^2 \]