At t=0, switch S is closed. The charge on the capacitor is varying with time as Q=Q0(1−e−αt). Obtain the value of Q0 and α in the given circuit parameters.
α=(R1+R2)R1R2C, Q0=CVR2R1+R2
Applying KVL,
V−IR1−qC=0
qC−(I−I1)R2=0
Also I1=dqdt
Solving the above equations,
q=VCR2(R1+R2)(1−e(R1+R2)tR1R2C)
α=(R1+R2)R1R2C
Q0=CVR2R1+R2