Superconducting resistive material

[Reshma]

In the given circuit, Resistance R is made up of type-I superconducting material with transition temperature T_c. The initial temperature of the circuit is T(>T_c). At time t=t₀ the temperature is dropped below T_c. Find the current in the circuit at:
1] at t<t₀ and through AB
2] at t=t₀
3] at t>t₀

My answer:

When the temperature is above the critical temperature, the circuit behaves normally. When the temperature is dropped below the crictical temperature, the resistance becomes R=0 and you get a persistent current. My problem is, I don't know what happens to the capacitor in the circuit once the temperature falls below T_c. Explanation needed...

 

[Reshma]

Come on guys, help me out here! I don't think it is that difficult.

 

[pseudovector]

The voltage on both the resistor and the capacitor should be equal to the battery's voltage at all times. I don't know what's a type I superconductor, but I assume it's resistance drops to 0 once it's temperature drops below Tc. Therefore, capacitor will always remain fully charged and no current will flow through it, but infinite current will flow through the rest of the circuit.

 

[Reshma]

The voltage on both the resistor and the capacitor should be equal to the battery's voltage at all times. I don't know what's a type I superconductor, but I assume it's resistance drops to 0 once it's temperature drops below Tc. Therefore, capacitor will always remain fully charged and no current will flow through it, but infinite current will flow through the rest of the circuit.

Thanks for replying!
Type I superconductors exhibit complete Meissner effect. I need to set up an equation to show that there is a persistent current in this circuit once the temperature falls below Tc. Any clues on how to proceed?