D’Sauty’s bridge is a type of bridge circuit used to measure the unknown value of capacitance. It consists of two identical capacitors (C1 and C2) in parallel, connected to a galvanometer and a variable resistor (R). The bridge is balanced when the galvanometer shows zero deflection, indicating that the unknown capacitance is equal to the known capacitance.

To understand why the correct answer is option 'C', let's examine the possible scenarios:

a) Possible to obtain balance even if both the capacitors are imperfect:
If both capacitors are imperfect, it means that their actual capacitance values are different from their nominal values. In this case, it is not possible to obtain balance because the bridge relies on the assumption that the capacitors are identical. Any difference in capacitance will result in an imbalance and a non-zero deflection on the galvanometer.

b) Possible to obtain balance if one of the capacitors is perfect:
If one of the capacitors is perfect, it means that its actual capacitance value is exactly equal to its nominal value. However, if the other capacitor is imperfect (i.e., its actual capacitance is different from its nominal value), the bridge will still be unbalanced. This is because the bridge requires both capacitors to be identical in order to achieve balance.

c) Possible to obtain balance only if both the capacitors are perfect:
This is the correct answer. In order to obtain balance in D’Sauty’s bridge, both capacitors must be perfect. This means that their actual capacitance values should exactly match their nominal values. When both capacitors are perfect, the bridge is balanced, and the galvanometer shows zero deflection.

d) All the above:
This option is not correct because it includes option 'a' and 'b', which have already been explained as incorrect. The correct answer is option 'C', as explained above.

In summary, D’Sauty’s bridge can only achieve balance if both capacitors are perfect, meaning their actual capacitance values match their nominal values. Any imperfection or difference in capacitance will result in an unbalanced bridge and a non-zero deflection on the galvanometer.