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Question

The circuit shown in the figure consists of a battery of emf E=10 V a capacitor of capacitance C=1.0 μF and three resistors of values R1=2 Ω, R2=2 Ω & R3=1 Ω. Initially, the capacitor is completely uncharged and the switch S is open. The switch S is closed at t=0. Then which of the following statements is/are correct?



A
The current through resistor R3 at the moment the switch closed is zero
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B
The current through resistor R3 a long time after the switch closed is 5 A
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C
The ratio of current through R1 & R2 is always constant
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D
The maximum charge on the capacitor during the operation is 5 μC
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Solution

The correct options are
A The current through resistor R3 at the moment the switch closed is zero
B The current through resistor R3 a long time after the switch closed is 5 A
C The ratio of current through R1 & R2 is always constant
D The maximum charge on the capacitor during the operation is 5 μC
Given,
E=10 V ; C=1.0 μFR1=2 Ω ; R2=2 Ω ; R3=1 Ω

Just after closing the switch, capacitor will act as wire. Thus, current through the resistor R3 is zero.


After closing the switch at t=, the capacitor will act as an open circuit.


Current through the battery is,

I=VR3+R1R2R1+R2=101+2×22+2=5 A

VAB=iR3=5 V

The maximum charge on the capacitor is,

Q=CV=1.0 μF×5 V=5 μC

Since, R1 & R2 are in parallel,

I1R1=I2R2

I1I2=R2R1=constant

Hence, all four options are correct.

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