Two capacitors of `3muF` and `6muF` are connected in series and a potential difference of 900 V is applied across the combination. They are then disconnected and reconnected in parallel. The potential difference across the combination is

Options

A. Zero
B. 100 V
C. 200 V
D. 400 V

Answer

To solve the problem step by step, we will first calculate the equivalent capacitance of the capacitors when they are connected in series, then find the charge stored, and finally determine the potential difference when they are connected in parallel.

### Step 1: Calculate the equivalent capacitance in series
When capacitors are connected in series, the formula for the equivalent capacitance \( C_{eq} \) is given by:

\[ \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} \]

For our capacitors, \( C_1 = 3 \mu F \) and \( C_2 = 6 \mu F \):

\[ \frac{1}{C_{eq}} = \frac{1}{3} + \frac{1}{6} \]

Finding a common denominator (which is 6):

\[ \frac{1}{C_{eq}} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2} \]

Thus,

\[ C_{eq} = 2 \mu F \]

### Step 2: Calculate the charge stored in the capacitors
The charge \( Q \) stored in the capacitors when a potential difference \( V \) is applied is given by:

\[ Q = C_{eq} \times V \]

Substituting the values:

\[ Q = 2 \mu F \times 900 V = 1800 \mu C \]

### Step 3: Reconnect the capacitors in parallel
When the capacitors are reconnected in parallel, the total capacitance \( C_{total} \) is the sum of the individual capacitances:

\[ C_{total} = C_1 + C_2 = 3 \mu F + 6 \mu F = 9 \mu F \]

### Step 4: Calculate the new potential difference across the parallel combination
The total charge \( Q \) remains the same when the capacitors are reconnected in parallel. We can use the formula for charge again:

\[ Q = C_{total} \times V_{new} \]

Rearranging this gives:

\[ V_{new} = \frac{Q}{C_{total}} = \frac{1800 \mu C}{9 \mu F} \]

Calculating \( V_{new} \):

\[ V_{new} = \frac{1800}{9} = 200 V \]

Thus, the potential difference across the combination when the capacitors are connected in parallel is **200 V**.

### Summary of Steps:
1. Calculate equivalent capacitance in series.
2. Calculate charge stored using the equivalent capacitance and applied voltage.
3. Calculate total capacitance when capacitors are connected in parallel.
4. Calculate new potential difference using the stored charge and total capacitance.