A series R-C combination is connected to an AC voltage of angular frequency (ω=500 radian/s). If the impedance of the R-C circuit is R√1.25, the time constant (in millisecond) of the circuit is?

Given : ω=500radian/s
Let the capacitance of the capacitor be C.
Thus resistance of capacitor XC=1/ωC=1/500C
Impedance of the circuit Z=R√1.25
Using Z²=R²+XC²
∴1.25R²=R²+1/(500)²C²
Or 0.25R²=1/(500)²C²
R²C²=1/(0.25)²(500)²
We get time constant of the circuit RC=1/(0.25)(500)=1/125=0.008s=8ms