JEE Physics 2023 Question with Solution

Step-by-step solution

Standard Method

Given: A capacitor combination is shown in the figure.

Find: The equivalent capacitance between the two terminals.

From the solution figure, capacitors (3) and (4) are short-circuited due to a direct conducting connection, so they do not affect the equivalent capacitance.

The remaining relevant capacitors are combined by identifying the parallel branch.

For capacitors in parallel,

$$C_{\text{eq}} = C_1 + C_2$$

Substituting the values shown in the solution,

$$C_{\text{eq}} = C + C = 2C$$

Therefore, the equivalent capacitance is $2C$.

The solution states The Correct Option is B, while the listed options show $2C$ as option D. Based on the working and final value, the correct option should correspond to $2C$.

Common mistakes

• Ignoring the short-circuit condition is a common mistake. A capacitor connected across a direct wire has zero potential difference across it, so it has no effect. Remove such capacitors before combining the circuit.

• Treating the remaining capacitors as series without checking the nodes is incorrect. First identify which capacitors share the same two nodes; only then decide whether they are in parallel or series.

• Following the option label from the solution without checking the actual value can lead to an error here. The working gives $2C$, so the value must be trusted over the mismatched printed option label.