1. The problem statement, all variables and given/known data Using the superposition principle, determine the current i(t. 2. Relevant equations Zc = 1/jwC Zl = jwL V = I*R I = V/Z 3. The attempt at a solution First, I converted inductor/capacitor to impedance: L = 1.5H -> jwL = j * 10 * 1.5 = 15j C = 10mf = 1/(jwC) = 1/(j*10*10*10^-3) = -0.1j Then, I transformed the 3A DC current source and 10 ohm resistor into a DC voltage source: I then shorted the 30V DC source to find i(t) with only Vs(t) = 10cos(10t)V After shorting the 30V DC source, C2 and R3 are in parallel. Their impedance is: (0.1j * 10)/(10-0.1j) = -j/(10-0.1j) After rationalizing: (0.1 - j)/100.01 Now that, L2 and R4 are in series, total impedance: 15j + 5 + (0.1 - j)/100.01 = (500.15-1499.15j)/100.01 = 15.8 < -71.55°. I = V/Z = (10<0°)/(15.88<-71.55° ) = 10/15.88<71.55°A Now I short the AC source: The DC source had a frequency of 0 rad/s, so the impedance of C3 is infinity (1/0) and L3 is 0 (j*0*L). The inductor is shorted and the capacitor is opened. There is a voltage source of 30V and a combined resistance of 15ohms. V=IR -> I = 30/15 = 2A<0° [(500.15/100.01 + 2) + (1499.15j/100.01)] Is 16.54<64.96° A the correct answer?