Two capacitor each having capacitance `C`and breakdown voltage `V`are joind in series .The capacitance and the breakdown voltage of the combination will be

Options

A. `2C and 2V`
B. `2C and 2V`
C. `2C and V`
D. `2C and V`

Answer

To solve the problem of finding the capacitance and breakdown voltage of two capacitors each having capacitance \( C \) and breakdown voltage \( V \) when connected in series, follow these steps:

### Step 1: Understand the Configuration
When capacitors are connected in series, the total capacitance decreases. Each capacitor in series has the same charge, and the total voltage across the series combination is the sum of the voltages across each capacitor.

### Step 2: Calculate the Total Capacitance
For two capacitors in series, the formula for total capacitance \( C' \) is given by:
\[ \frac{1}{C'} = \frac{1}{C_1} + \frac{1}{C_2} \]
Since both capacitors have the same capacitance \( C \):
\[ \frac{1}{C'} = \frac{1}{C} + \frac{1}{C} = \frac{2}{C} \]
Thus, we can find \( C' \):
\[ C' = \frac{C}{2} \]

### Step 3: Calculate the Total Breakdown Voltage
The total breakdown voltage \( V' \) for capacitors in series is the sum of the breakdown voltages of each capacitor:
\[ V' = V_1 + V_2 \]
Since both capacitors have the same breakdown voltage \( V \):
\[ V' = V + V = 2V \]

### Conclusion
The capacitance of the combination is \( \frac{C}{2} \) and the breakdown voltage is \( 2V \).

### Final Answer
The combination of the two capacitors in series has:
- Capacitance: \( \frac{C}{2} \)
- Breakdown Voltage: \( 2V \)

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