Solving Circuit Analysis Problem: Finding R and V(t) for Given Conditions

[whatphysics]

There is a question I am not sure of how I should start/approach. Any help would be appreciated, thanks.

Vc(0)=3V and ic(t)=e^-50t for t>0 and t=0. Find the value of R and voltage v(t) for t>0 and t=0

 

[person_random_normal]

Apply Kirchhoff' Voltage rule in the two loops ,
first in the loop with 2 ohm resis. and capacitor to find voltage
and then in the loop with 2 resistors (R and 2 ohm) to find R !

 

[gneill]

I might start by examining the form of the capacitor current. There's a time constant that will have to involve the value of R in some way... Are you familiar with Thevenin equivalents? What resistance will the capacitor "see" when it's following ic(t)=e^-50t ? Can you disentangle R from that?