So I have the circuit below and this is the information given: Load 1 absorbs 4203.22-2835.11j [VA] Voltage sources delivers 7500 [W] v_s(t) = 400cos(100[rad/s]t+38°) [V] Find all possible values for L_A So my idea was to put it into phasor domain. So V_s=400<38° Since the voltage source only delivers power the angle of voltage and current have to be the same since the power factor is 1 so I came up with S_L=.5(V_s)(I_L*) (Complex Power Formula) So I_L=(7500/400*2)<38° = 37.5<38° Then I could find the voltage of the Load and that comes out to be Using S_L=.5(V_L)(I_L*) V_L= 2*(4203.2-2835.1j)/(37.5<38°) V_L= 269.744+18.86j After that i thought I could just do a KVL to get the value for L_A (the inductor) So KVL -V_s+(L_A+R_1)(I_L)+V_L=0 So I get -400<38°+37.5<38°(100LjΩ+3.3Ω)+ 269.744+18.86j = 0 But this does not give me a real value for L_A, I am getting a complex value For reference the answer is 77.1 [mH]
you did not post original question (please post it exactly "as is") and reading though your comment gives me a headache ;-) 7500W is P not S. S is measured in VA not W. you have there series circuit so current is the same in L, R and load. note that: Psource=Presistor+Pload 7500 = Presistor + 4203.22 Presistor = 3296.78W I=sqrt(Presistor/R)=31.607A but this is only magnitude of RMS current, we don't know the angle of it yet. similarly, Rload=Pload/I^2=4.2074 Ohm Re(Z)=R+Rload = 3.3+4.2074=7.5074 Ohm