CapacitanceHard
Question
Capacitor C1 of the capacitance 1 microfarad and capacitor C2 of capacitance 2 microfarad are separately charged fully by a common battery. The two capacitors are then separately allowed to discharge through equal resistors at time t = 0.
Options
A.the current in each of the two discharging circuits is zero at t = 0.
B.the current in the two discharging circuits at t = 0 are equal but non zero.
C.the current in the two discharging circuits at t = 0 are unequal
D.capacitor C1 loses 50% of its initial charge sooner than C2 loses 50% of its initial charge
Solution
During decay of charge in RC circuit
I = I0e−t/RC
where
when t = 0, I =
Since potential difference between the plates is same initially therefore I same in both the cases at t = 0 and is equal to
Also
Also q = q0e−t/RC. When q =
then 
= q0e−t/RC
⇒ e+t/RC = 2.
= ln2
⇒ t = RC loge 2
⇒ t ∞ C. Therefore time taken for the first capacitor (1μF) for discharging 50% of Initial charge will be less.
(B), (D) are the correct options.
I = I0e−t/RC
where
when t = 0, I =
Since potential difference between the plates is same initially therefore I same in both the cases at t = 0 and is equal to
Also
Also q = q0e−t/RC. When q =
then = q0e−t/RC ⇒ e+t/RC = 2.
= ln2⇒ t = RC loge 2
⇒ t ∞ C. Therefore time taken for the first capacitor (1μF) for discharging 50% of Initial charge will be less.
(B), (D) are the correct options.
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