Three condensers each of capacity C microfarad are connected in series. An exactly similar set is connected in parallel to the first one. The effective capacity of the combination is `4 muF`. Then, the value of C in microfard is

Options

A. 8
B. 6
C. 4
D. 2

Answer

To solve the problem, we need to find the value of C in microfarads given that three capacitors of capacity C each are connected in series, and another identical set is connected in parallel to the first one, resulting in an effective capacity of 4 µF.

### Step-by-Step Solution:

1. **Understand the Configuration**:
- We have two sets of capacitors.
- Each set contains three capacitors (C) connected in series.
- The two sets are connected in parallel.

2. **Calculate the Equivalent Capacitance for One Set in Series**:
- 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 capacitors have the same capacitance C:
\[ \frac{1}{C_{eq}} = \frac{1}{C} + \frac{1}{C} + \frac{1}{C} = \frac{3}{C} \]
- Therefore, the equivalent capacitance for one set of three capacitors in series is:
\[ C_{eq} = \frac{C}{3} \]

3. **Calculate the Equivalent Capacitance for Both Sets in Parallel**:
- Since we have two sets of capacitors in series (each with capacitance \( \frac{C}{3} \)) connected in parallel, the total equivalent capacitance (C_total) is:
\[ C_{total} = C_{eq1} + C_{eq2} = \frac{C}{3} + \frac{C}{3} = \frac{2C}{3} \]

4. **Set Up the Equation**:
- We are given that the effective capacity of the combination is 4 µF:
\[ \frac{2C}{3} = 4 \]

5. **Solve for C**:
- To find C, multiply both sides by 3:
\[ 2C = 12 \]
- Now, divide by 2:
\[ C = 6 \, \text{µF} \]

### Final Answer:
The value of C is **6 µF**.