# Circuit Theory/Phasors/Examples/example14

< Circuit Theory | Phasors | Examples

< Circuit Theory | Phasors | Examples

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.

- 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:
- $v_{2}=r_{1}*i_{2}$
- $i_{3}=c_{1}{d \over dt}v_{3}$
- $v_{9}=r_{3}*i_{6}$
- $v_{6}=L_{1}*{d \over dt}i_{2}$
- $i_{4}=c_{2}{d \over dt}v_{4}$
- $v_{5}=L_{2}*{d \over dt}i_{5}$
- $v_{7}=r_{2}*i_{1}$
- $i_{2}+I_{1}-i_{3}=0$
- $i_{3}-I_{4}-i_{6}=0$
- $i_{4}-i_{1}-i_{5}=0$
- $v_{1}+v_{2}+v_{3}+v_{9}+v_{6}-V_{1}=0$
- $v_{4}+v_{5}-v_{9}=0$
- $v_{7}+v_{3}+v_{4}-v_{8}=0$