The instantaneous value of emf and current in an A.C. circuit are; E=1.414sin(100πt− 4 π ​ ) , I=0.707sin(100πt) . The impedance of the circuit will be

Explanation

Inductive reactance,
`X_L=omegaL=(2pi)(50)(35times10^-3)approx11Omega`
Impedance, `Z=sqrt(R^2+X_L^2)=sqrt(11^2+11^2)=11sqrt2Omega`
Given `V_(rms)=220V`
Hence amplitude of voltage, `V_0=sqrt2V_(rms)=220sqrt2V`
`therefore` Amplitude of current ,`I_0=V_0/Z=(220sqrt2)/(11sqrt2)=20A`
Please difference between the current and the voltage in the circuit,
`theta=tan^-1(X_L/R)=tan^-1(11/11)=pi/4`
In LR circuit, voltage leads the current by phase angle `theta`. Thus current in the circuit,
`I=I_0sin(omegat-theta)=20sin(omegat-pi/4)`