A 110 resistor a 2mH coil and a 003 F capacitor are in paral

A 110 resistor, a 2-mH coil and a 0.03 F capacitor are in parallel across a 200 V 10 kHz ac source.Find the reactance of the capacitor.Find the reactance of the coil.Find the phasor current drawn by each branch (Resistor, coil, capacitor).Find the total current.Find the power drawn by the circuit.

Solution

reactance of the coil xl=jwl=j2*3.14*10*10^3*2*10^-3=j125.66 ohms

reactance of the capacitor xc=1/(jwc)=1/(j2*3.14*10*10^3*0.03*10^-6)=-j530.5 ohms

total admittance=1/110+1/j125.66+1/(-j530.5)=(9.09*10^-3-j6.07*10^-3) mhos

total impedance=1/total admittance=1/(9.09*10^-3-j6.07*10^-3)=(76.05+j50.808) ohms

total current=200<0/(76.05+j50.808)=2.186<-33.746 amps

total power drawn by the circuit=(2.186<-33.746)*(200<0)=437.2<-33.746 watts.