Circuit Theory/Phasors/Examples/example14

Complex 3R, 2L, 2C, voltage and current source circuit

Given that the voltage source is defined by $V_s(t)=10cos(1000t+30^{\circ })$ and the current source is defined by $I_s(t)=0.5sin(1000t+45^{\circ })$, find all other voltages, currents and power of the sources.

Circuit marked up for analysis

Knowns, Unknowns and Equations

Knowns: $v_1,R_1,R_2,R_3,L_1,L_2,C_1,C_2,i_1$

Unknowns: $v_2,v_3,v_4,v_5,v_6,v_7,v_8,v_9,i_2,i_3,i_4,i_5,i_6$

Equations:

$v_2=r_1*i_2$

$i_3=c_1\frac{d}{dt}{v}_3$

$v_9=r_3*i_6$

$v_6=L_1*\frac{d}{dt}{i}_2$

$i_4=c_2\frac{d}{dt}{v}_4$

$v_5=L_2*\frac{d}{dt}{i}_5$

$v_7=r_2*i_1$

$i_2+I_1-i_3=0$

$i_3-I_4-i_6=0$

$i_4-i_1-i_5=0$

$v_1+v_2+v_3+v_9+v_6-V_1=0$

$v_4+v_5-v_9=0$

$v_7+v_3+v_4-v_8=0$

Solutions and Analysis

numeric solution calculated in the phasor domain

simulation at circuitlab