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Question

A series RC combination is connected to an ac voltage of angular frequency ω=500 rad/s. If the impedance of the R-C circuit is R1.25, the time constant (in millisecond) of the circuit is

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Solution

As we know that the time constant is given as, τ=RC, so we have to calculate resistance as well as capacitance.
Impedance is given, Z=R1.25 and we know the phase difference between R and XC is π2.
(R1.25)2=R2+X2C
0.25R2=X2C
XC=0.5R
as we know,
XC=1ωC
C=1500×0.5R=1250R
RC=1250=4×103 s
τ=RC=4 ms

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