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=R√1.25 and we know the phase difference between R and XC is π2.
(R√1.25)2=R2+X2C
0.25R2=X2C
XC=0.5R
as we know,
XC=1ωC
C=1500×0.5R=1250R
RC=1250=4×10−3 s
τ=RC=4 ms