For the circuit shown below Given it im cosomegat Find i1t

For the circuit shown below: Given: i(t) = i_m cos(omegat) Find i_1(t). Values:

xc=1/(jwc)=1/(j10000*0.8*10^-6)=-j125 ohms

xl1=jwl1=j10000*11.6*10^-3=j116 ohms

xl2=jwl2=j10000*15.4*10^-3=j154 ohms

apply nodal analysis

(v/-j125)+[v/(500+j116)]+(v/j154)=22*10^-3<0+[(0.25*v)/(500+j116)]

v[(1/-j125)+1/(500+j116)+1/j154-0.25/(500+j116)]=22*10^-3<0

v*{[(500+j116)*j154+j154*-j125+(500+j116)*-j125+0.25*j154*j125]/[(500+j116)*j154*-j125]}=22*10^-3<0

v=8.6<-21.9 volts

current i1=v/(r+jxl1)=8.6<-21.9/(500+j116)=0.016<-34.96 amps