If the capacitors in the previous question are joined in parallel,the capacitance and the breakdown voltage of the combination will be

Options

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

Answer

To solve the problem of finding the capacitance and breakdown voltage of two capacitors connected in parallel, we can follow these steps:

### Step 1: Understand the configuration
When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitances.

### Step 2: Write the formula for total capacitance
For two capacitors \( C_1 \) and \( C_2 \) connected in parallel:
\[ C_{\text{equiv}} = C_1 + C_2 \]

### Step 3: Substitute the values
Given that both capacitors have the same capacitance \( C \):
\[ C_{\text{equiv}} = C + C = 2C \]

### Step 4: Determine the breakdown voltage
In a parallel connection, the voltage across each capacitor is the same and is equal to the applied voltage \( V \). Therefore, the breakdown voltage of the combination remains the same as that of each capacitor:
\[ V_{\text{breakdown}} = V \]

### Step 5: State the final results
Thus, the total capacitance of the combination is \( 2C \) and the breakdown voltage is \( V \).

### Final Answer:
The capacitance and the breakdown voltage of the combination will be \( 2C \) and \( V \).

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