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Capacitor C1 of capacitance 1 micro-fara...

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.

Text Solution

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During discharging of condenser,
`q = q_(0) e^(-t//RC)`
and `i= (E_(0) e^(-t//RC))/(R )`
is same in the two cases.
Also, R is same as they are discharged through equal resistors.
`:.` At `t = 0, i= (E_(0))/(R ) e^(0) = (E_(0))/(R ) =` constant
Hence, current in the two discharging circuits at `t = 0` are equal but not zero.
Now, time constant, `tau = RC`
As `C_(2) gt C_(1)`, therefore `tau_(2) gt tau_(1)`, or `tau_(1) lt tau_(2)`, i.e.,
`C_(1)` would lose charge faster than `C_(2)`. Hence alternatives (b) and (d) are correct.
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