Circuit Theory/Phasors/Examples/example11

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.



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:
 * $$ v_1 = R_1 * i_1$$
 * $$ v_2 = R_2 * i_2$$
 * $$ i_C = C * {d \over dt}v_C$$
 * $$ v_L = L * {d \over dt}i_L$$
 * $$ i_1 + I_s - i_2 -i_C = 0$$
 * $$ i_c - I_s - i_L = 0$$
 * $$ v_1 + v_2 - V_s = 0$$
 * $$ v_C + v_L - v_2 = 0$$

Solutions and Analysis

 * numeric solution calculated in the phasor domain
 * attempt at a Laplace solution
 * simulation at circuitlab