In the shown circuit involving a resistor of resistance R Ω , capacitor of capacitance C farad and an ideal cell of emf E volts, the capacitor is initially uncharged and the key is in position 1. At t = 0 second the key is pushed to position 2 for t 0 = RC seconds and then key is pushed back to position 1 for t 0 = RC seconds. This process is repeated again and again. Assume the time taken to push key from position 1 to 2 and vice versa to be negligible.
(i) The charge on capacitor at t = 2RC second is
(ii) The current through the resistance at t = 1.5 RC seconds is 
(iii) Then the variation of charge on capacitor with time is best represented by 
Text Solution
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(i)
(ii)
(ii)
Sol. For t = 0 to t o = RC seconds, the circuit is of charging type. The charging equation for this time is
Therefore the charge on capacitor at time t 0 = RC is 
For t = RC to t = 2RC seconds, the circuit is of discharging type. The charge and current equation for this time are
and 
Hence charge at t = 2 RC and current at t = 1.5 RC are
and 
respectively
Since the capacitor gets more charged up from t = 2RC to t= 3RC than in the interval t=0 to t=RC, the graph representing the charge variation is as shown in figure
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