The correct answer is: C. the bridge can be balanced if the resistances have some specific values.
A Wheatstone bridge is a circuit arrangement that can be used to measure an unknown electrical resistance by balancing two legs of a bridge circuit. When the bridge is balanced, the current through the galvanometer is zero.
In the case of a bridge with an inductance in one arm and resistances in the remaining three arms, the bridge can be balanced if the resistances have some specific values. These values depend on the inductance and the frequency of the applied voltage.
If the resistances are not equal, the bridge will be unbalanced and there will be a current through the galvanometer. The amount of current will depend on the magnitude of the resistance imbalance.
The following is a brief explanation of each option:
- Option A: The bridge can always be balanced. This is not true. The bridge can only be balanced if the resistances have some specific values.
- Option B: The bridge cannot be balanced. This is also not true. The bridge can be balanced if the resistances have some specific values.
- Option C: The bridge can be balanced if the resistances have some specific values. This is the correct answer.
- Option D: None of the above. This is not true. The bridge can be balanced if the resistances have some specific values.