It is given that when switch S is open, charge on one of the capacitors is q′=cε2 and another one is zero. At t = 0 switch S is closed, then
A
Current i through R is i=εRe−2tRC
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B
Charge on capacitor C2 is εC2(2−e−2tRC)
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C
Heat generated across R in long time is ε2C16
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D
Charge on capacitor C1 is εC4(1−e−2tRC)
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Solution
The correct options are C Heat generated across R in long time is ε2C16 D Charge on capacitor C1 is εC4(1−e−2tRC) By K.V.L: ε=iR+qC+q+q′C As q′c=ε2 ε2−2qc=iR
As i=dqdt εC−4q2CR=dqdt⇒∫q0dqεC−4q=∫t0dt2RC q=εC4(1−e−2tRC) ∴i=dqdt=ε2Re−2tRC So, heat generated after a long duration, H=∫∞0i2Rdt=ε2C16