Question: 22. The equivalent capacitance of the combination shown in the figure is :
(1) 3 C
(2) 2\mathrm{C}
(3) \mathrm{C}/2
(4) 3\mathrm{C}/2
Answer: Option (2)
Explanation:
All the capacitors shown in the circuit have the same capacitance C.
The left and right terminals are connected by two horizontal branches.
The top branch contains one capacitor C and the bottom branch also contains one capacitor C.
These two branches are connected between the same pair of points, hence they are in parallel.
The equivalent capacitance of the two parallel capacitors is given by C_p = C + C = 2C.
The vertical capacitor in the middle is connected between the same two nodes as the parallel combination, so it is also in parallel with them.
Thus, the total equivalent capacitance is C_{\text{eq}} = 2C + C.
However, the top and bottom capacitors form a conducting loop that makes the potential difference across the middle capacitor zero, so it does not contribute to the equivalent capacitance.
Therefore, the effective capacitance of the circuit is C_{\text{eq}} = 2C.
Hence, the correct answer is Option (2).