Question

Find the equivalent capacitance across points A and B in the given electric circuit.

• A. \(\frac{C}{2}\)
• B. 2C
• C. \(\frac{5C}{3}\)
• D. \(\frac{3C}{4}\)

Hint:

Identify the shorted capacitors, and notice they have no effect on the overall cir cuit. Then, simplify the circuit by combining parallel capacitances. The formula for parallel capacitance is Ceq = C1 + C2 + ...

Answer 1

The Correct Option is B

Step 1: Identify Connections

• Capacitors (3) and (4) are short-circuited due to a direct connection and can be ignored.
• This leaves capacitors \( C_1 \), \( C_2 \), and two other capacitors (\( \frac{C}{3} \) and \( C \)).

Step 2: Parallel Combination of \( C_1 \) and \( C_2 \)

The capacitance for a parallel combination is given by:

\[ C_{\text{eq}} = C_1 + C_2 \]

Substituting \( C_1 = C \) and \( C_2 = C \):

\[ C_{\text{eq}} = C + C = 2C \]

Step 3: Simplified Circuit

After combining \( C_1 \) and \( C_2 \), the equivalent circuit consists of a total capacitance of \( 2C \) in parallel with the remaining components.

Conclusion:

The equivalent capacitance of the circuit is \( 2C \).