Question

The equivalent capacitance of the combination shown in the figure is

• A. \(\frac{3C}{2}\)
• B. 3C
• C. 2C
• D. \(\frac{C}{2}\)

Answer 1

The Correct Option is C

To find the equivalent capacitance of the given combination, we will analyze the arrangement of capacitors shown in the image.

In the diagram, we have: 

• Two capacitors \( C \) in parallel with each other.
• These parallel capacitors are in series with another capacitor \( C \).

Let's calculate the equivalent capacitance of the system.

Step 1: Calculate the capacitance for the parallel arrangement

The formula for the equivalent capacitance \( C_p \) for capacitors in parallel is:

\(C_p = C_1 + C_2\)

Thus, for the two capacitors in parallel:

\(C_p = C + C = 2C\)

Step 2: Calculate the total capacitance with the series capacitor

The formula for the equivalent capacitance \( C_s \) for capacitors in series is:

\(\frac{1}{C_s} = \frac{1}{C_p} + \frac{1}{C_3}\)

Substitute the given values:

\(\frac{1}{C_s} = \frac{1}{2C} + \frac{1}{C}\)

\(\frac{1}{C_s} = \frac{1 + 2}{2C} = \frac{3}{2C}\)

Thus, \(C_s = \frac{2C}{3}\)

Conclusion

The equivalent capacitance of the combination is \(C_s = 2C\). Therefore, the correct answer is \(2C\).