Circuit Theory/Phasors/Examples/example11

Complex 2R, L, C, voltage circuit

Given that the voltage source is defined by $V_s(t)=cos(t)$ and the current source is defined by $I_s(t)=2sin(t-\frac{\pi }{3})$, find all other voltages, currents and check power.

Circuit marked up for analysis

Knowns, Unknowns and Equations

Knowns: $V_s,R_1,R_2,L,C,I_s$

Unknowns: $v_1,v_2,v_C,v_L,i_1,i_2,i_C,i_L$

Equations:

$v_1=R_1*i_1$

$v_2=R_2*i_2$

$i_C=C*\frac{d}{dt}{v}_C$

$v_L=L*\frac{d}{dt}{i}_L$

$i_1+I_s-i_2-i_C=0$

$i_c-I_s-i_L=0$

$v_1+v_2-V_s=0$

$v_C+v_L-v_2=0$

Solutions and Analysis

numeric solution calculated in the phasor domain

attempt at a Laplace solution

simulation at circuitlab