A capacitor C1 of capacitance 1microF and a capacitor of capacitance 2microF are separately charged by a common battery for a long time. The two capacitors are then separately charged through equal resistors. Both the discharge circuits are connected at t=0. Then (multiple choice qstn) (a) the current in each of the two discharging circuits is 0 at t=0 (b) the currents in the two discharging circuits at t=0 are equal but not 0 (c) the currents in the two discharging circuits at t=0 are unequal (d) C1 loses 50% of its initial charge sooner than C2 loses 50% of its initial charge

As in case of discharging of a capacitor though a resistance
q = q0*e^-t/CR
i = -dq/dt = (q0/CR)*e^-t/CR
at t = 0, i = q0 / CR
we know q0 = CV
so i = CV / CR
i = V / R
i.e. the current at t = 0 is independent of capacitance in the circuit and as here V and R is same for both the circuit, the current at t = 0 will be same [t V/R] and maximum in both the circuits.
In case of discharging of a capacitor through a resistance as
q = q0*e^-t/CR
t = CR loge [q0 / q]
So time taken for 50% of the charge to leak through the resistance


i.e. the capacitor C₁ will be lose its 50% charge sooner than CO₂
Hence option (b) and (d) are correct
Thanks & Regards,
Nirmal Singh
Askiitians Faculty

Approved

thanku :)