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`

Answer

To solve the problem of finding the 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: Calculate the Equivalent Capacitance
When capacitors are connected in series, the formula for the equivalent capacitance \( C_{eq} \) is given by:

\[ \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} \]

For three capacitors of the same capacitance \( C \):

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

Taking the reciprocal gives us:

\[ C_{eq} = \frac{C}{3} \]

### Step 2: Calculate the Breakdown Voltage
In a series connection, the total breakdown voltage \( V_{eq} \) is the sum of the breakdown voltages of the individual capacitors. Since each capacitor has a breakdown voltage of \( V \):

\[ V_{eq} = V_1 + V_2 + V_3 = V + V + V = 3V \]

### Final Results
Thus, the equivalent capacitance and breakdown voltage of the combination are:

- **Capacitance**: \( C_{eq} = \frac{C}{3} \)
- **Breakdown Voltage**: \( V_{eq} = 3V \)

### Summary
The final answer is:
- Equivalent Capacitance: \( \frac{C}{3} \)
- Equivalent Breakdown Voltage: \( 3V \)

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