Capacitor `C_1` of capacitance 1 micro-farad and capacitor `C_2` of capacitance 2 microfarad are separately charged fully by a common battery. The two capacitors are then separately allowed to discharged through equal resistors at time t = 0.

Options

A. (i),(iv)
B. (ii),(iv)
C. (iii),(iv)
D. (i),(ii)

Answer

A

Explanation

`C_(1)= 1muF, C_(2) = 2 mu F`
`q = q_(0)e^(-t//RC)`
`q_(1) = C_(1)Ee^(-t//RC_1) implies i_(1) = (dq_1)/(dt) = E/R e^(-t//RC_1)`
`q_(2) = C_(2) Ee^(-t//RC_1) implies i_(2) = -(dq_2)/(dt) = E/R e^(-t//RC_2)`
`t = 0 . i_(1)=i_(2) (i)` is O.K.
`q_(1) = C_(1) Ee^(-t//RC_1) implies (C_1E)/(2) = C_(1)e^(-t_(1)//Rxx1)`
`e^(t_1//R) = 2 implies t_(1) = R 1n2`
`q_(2) = C_(2) Ee^(-t//RC_2) implies (C_2E)/(2) = C_(2)Ee^(-t_2//2R)`
`e^(t_2//2R) = 2implies t_(2) = 2 R 1n 2`
`t_(1) lt t_(2) (iv)` is O.K.