Find the steadystate expression for vo in the circuit of Fig

Find the steady-state expression for vo in the circuit of (Figure 1) if ig=90cos10000tmA. Suppose that vo(t)=V0cos(?t+?), where ?180?<??180?. Determine the values V0, ?, ?.

Express your answers using three significant figures separated by commas.

Solution

from the circuit

w=10,000

Xl=jwl=j10,000*10*10^-3=j100 ohms

xc=1/(jwc)=1/(j10,000*2*10^-6)=-j50 ohms

current through 2uf capacitor is

i=[{90<0*(50+j100)}/{50+j100+100-j50}]

i=63.639<45 amps

vo=100*63.639<45

vo=6363.9<45 volts

vo(t)=6363.9cos(10000t+45) volts

vo=6363.9

w=10000

q=45 degrees