Three identical capacitors, each of capacitance `C`, are connected in series with a battery of emf `V` and get fully charged. Now the battery is removed and the capacitors are cannected in parallel with positive terminals at one point and negative terminals at other point. Then, The connon potintial will be.

Options

A. `V`
B. `3V`
C. `V//3`
D. zero

Explanation

To solve the problem step by step, let's break it down:

### Step 1: Understand the Initial Configuration
Three identical capacitors, each with capacitance \( C \), are connected in series to a battery with an emf \( V \).

### Step 2: Calculate the Equivalent Capacitance in Series
When capacitors are connected in series, the equivalent capacitance \( C_{eq} \) can be calculated using the formula:
\[ \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} \]
Since all capacitors are identical and have capacitance \( C \):
\[ \frac{1}{C_{eq}} = \frac{1}{C} + \frac{1}{C} + \frac{1}{C} = \frac{3}{C} \implies C_{eq} = \frac{C}{3} \]

### Step 3: Calculate the Charge on the Capacitors
The charge \( Q \) on the equivalent capacitor when connected to the battery is given by:
\[ Q = C_{eq} \cdot V = \left(\frac{C}{3}\right) \cdot V = \frac{CV}{3} \]
Since the charge is the same on each capacitor in series, each capacitor will have a charge \( Q = \frac{CV}{3} \).

### Step 4: Determine the Voltage Across Each Capacitor
The voltage across each capacitor \( V' \) can be calculated using the formula:
\[ V' = \frac{Q}{C} = \frac{\frac{CV}{3}}{C} = \frac{V}{3} \]
Thus, each capacitor has a voltage of \( \frac{V}{3} \).

### Step 5: Disconnect the Battery and Connect Capacitors in Parallel
After charging, the battery is removed, and the capacitors are connected in parallel. In a parallel connection, the voltage across each capacitor remains the same.

### Step 6: Calculate the Common Potential in Parallel
When the capacitors are connected in parallel, the common potential \( V_{common} \) will be the same across all capacitors. Since each capacitor was charged to \( \frac{V}{3} \), the common potential will also be:
\[ V_{common} = \frac{V}{3} \]

### Final Answer
The common potential when the capacitors are connected in parallel is:
\[ \boxed{\frac{V}{3}} \]