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Question

In the figure shown below, R1=1Ω , R2=2Ω , C1=4μF , C2=2μF , the time constants (in μs) for the circuits I ,II and III respectively are


A
18 , 4, 89
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B
18 , 89 , 2
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C
18 , 89 , 4
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D
4 , 89 , 18
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Solution

The correct option is C 18 , 89 , 4
All the three circuits given are RC circuits. Therefore, the time constant for each circuit is RC.

Finding the equivalent resistance and capacitance for all three given circuits,

For first circuit:

Req=1+2=3Ω ; Ceq=4+2=6μF

For second circuit:

R′′eq=1×21+2=23Ω ; C′′eq=4×24+2=43μF

For third circuit:

R′′′eq=1×21+2=23Ω ; C′′′eq=4+2=6μF

Time constant in first circuit , τ1=ReqCeq=18μs

Time constant in second circuit , τ2=R′′eqC′′eq=89μs

Time constant in third circuit , τ3=R′′′eqC′′′eq=4μs

Hence, option (c) is the correct answer.

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