Given that the voltage source is defined by V s ( t ) = c o s ( t ) {\displaystyle V_{s}(t)=cos(t)} and the current source is defined by I s ( t ) = 2 s i n ( t − π 3 ) {\displaystyle I_{s}(t)=2sin(t-{\frac {\pi }{3}})} , find all other voltages, currents and check power. Knowns: V s , R 1 , R 2 , L , C , I s {\displaystyle V_{s},R_{1},R_{2},L,C,I_{s}} Unknowns: v 1 , v 2 , v C , v L , i 1 , i 2 , i C , i L {\displaystyle v_{1},v_{2},v_{C},v_{L},i_{1},i_{2},i_{C},i_{L}} Equations: v 1 = R 1 ∗ i 1 {\displaystyle v_{1}=R_{1}*i_{1}} v 2 = R 2 ∗ i 2 {\displaystyle v_{2}=R_{2}*i_{2}} i C = C ∗ d d t v C {\displaystyle i_{C}=C*{d \over dt}v_{C}} v L = L ∗ d d t i L {\displaystyle v_{L}=L*{d \over dt}i_{L}} i 1 + I s − i 2 − i C = 0 {\displaystyle i_{1}+I_{s}-i_{2}-i_{C}=0} i c − I s − i L = 0 {\displaystyle i_{c}-I_{s}-i_{L}=0} v 1 + v 2 − V s = 0 {\displaystyle v_{1}+v_{2}-V_{s}=0} v C + v L − v 2 = 0 {\displaystyle v_{C}+v_{L}-v_{2}=0} numeric solution calculated in the phasor domain attempt at a Laplace solution simulation at circuitlab
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