Two parallel plate condenser A and B having capacitances of `1 mu F and 5 mu F` are charged separately to the same potential of 100V. Now the positive plate of A is connected to the negative plate of B and the negative plate of A to the positive plate of B.
Energy stored in capacitor is

Options

A. `2 times 10^-2 J`
B. `3 times 10^-2 J`
C. `4 times 10^-4 J`
D. `5 times 10^-5 J`

Answer

To solve the problem, we will follow these steps:

### Step 1: Identify the given values
We have two capacitors:
- Capacitor A: \( C_A = 1 \, \mu F = 1 \times 10^{-6} \, F \)
- Capacitor B: \( C_B = 5 \, \mu F = 5 \times 10^{-6} \, F \)
Both capacitors are charged to the same potential:
- Voltage \( V = 100 \, V \)

### Step 2: Calculate the charge on each capacitor
The charge \( Q \) stored in a capacitor is given by the formula:
\[ Q = C \times V \]
For capacitor A:
\[ Q_A = C_A \times V = (1 \times 10^{-6} \, F) \times (100 \, V) = 1 \times 10^{-4} \, C \]
For capacitor B:
\[ Q_B = C_B \times V = (5 \times 10^{-6} \, F) \times (100 \, V) = 5 \times 10^{-4} \, C \]

### Step 3: Connect the capacitors
When the positive plate of capacitor A is connected to the negative plate of capacitor B and the negative plate of capacitor A is connected to the positive plate of capacitor B, they are effectively connected in parallel.

### Step 4: Calculate the net capacitance
The total capacitance \( C_{net} \) for capacitors in parallel is the sum of their capacitances:
\[ C_{net} = C_A + C_B = 1 \, \mu F + 5 \, \mu F = 6 \, \mu F = 6 \times 10^{-6} \, F \]

### Step 5: Calculate the energy stored in the combined capacitor
The energy \( U \) stored in a capacitor is given by the formula:
\[ U = \frac{1}{2} C V^2 \]
Using the net capacitance and the voltage:
\[ U = \frac{1}{2} \times C_{net} \times V^2 = \frac{1}{2} \times (6 \times 10^{-6} \, F) \times (100 \, V)^2 \]
Calculating this gives:
\[ U = \frac{1}{2} \times (6 \times 10^{-6}) \times (10000) = 3 \times 10^{-2} \, J \]

### Final Answer
The energy stored in the capacitor is:
\[ U = 3 \times 10^{-2} \, J \]

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