Three capacitors each of capacitance `C` and of breakdown voltage `V` are joined in series. The capacitance and breakdown voltage of the combination will be

Options

A. `(C )/(3), (V)/(3)`
B. `3C, (V)/(3)`
C. `(C )/(3), 3V`
D. `3C, 3V`

Explanation

To solve the problem of finding the equivalent capacitance and breakdown voltage of three capacitors, each with capacitance \( C \) and breakdown voltage \( V \), connected in series, we can follow these steps:

### Step 1: Understand the Configuration
Three capacitors are connected in series. In a series configuration, the total or equivalent capacitance is different from that of capacitors connected in parallel.

### Step 2: Calculate the Equivalent Capacitance
For capacitors in series, the formula for equivalent capacitance \( C_{eq} \) is given by:
\[ \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} \]
Since all three capacitors have the same capacitance \( C \):
\[ \frac{1}{C_{eq}} = \frac{1}{C} + \frac{1}{C} + \frac{1}{C} = \frac{3}{C} \]
Thus, we can find \( C_{eq} \) by taking the reciprocal:
\[ C_{eq} = \frac{C}{3} \]

### Step 3: Calculate the Breakdown Voltage
The breakdown voltage for capacitors in series is the sum of the individual breakdown voltages. Since each capacitor has a breakdown voltage \( V \):
\[ V_{eq} = V + V + V = 3V \]

### Final Result
The equivalent capacitance and breakdown voltage of the combination of the three capacitors in series are:
\[ C_{eq} = \frac{C}{3} \quad \text{and} \quad V_{eq} = 3V \]

### Summary
- **Equivalent Capacitance**: \( \frac{C}{3} \)
- **Equivalent Breakdown Voltage**: \( 3V \)