Let and . Let denote the charge on the positive side of the the capacitor and let denote the charge on the positive side of the capacitor. Let denote the voltage across the capacitor and let denote the voltage across the capacitor. Let denote the total resistance of the wire (so R include the resistance from both of the two disconnected sections of the wire).
The current must be the same everywhere in the circuit. Therefore, the rate at which positive charges leave the capacitor must equal the rate at which positive charges leave the capacitor. That is
This implies that
Initially, and . So, .
The current through the resistor must be zero when the circuit reaches a steady state, so the magnitudes of the voltages across the capacitors must be equal, and their sign must be opposite (because of Kirchhoff's voltage law). That is,
The solution to the system of equations and is and .
Therefore answer (C) is correct.