Complex 3R, 2L, 2C, voltage and current source circuit
Given that the voltage source is defined by
and the current source is defined by
, find all other voltages, currents and power of the sources.
Circuit marked up for analysis
- Knowns:
![{\displaystyle v_{1},R_{1},R_{2},R_{3},L_{1},L_{2},C_{1},C_{2},i_{1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3d3a3502d4ed6c35a999d6493d0495e28b69ad34)
- Unknowns:
![{\displaystyle 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}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d8fad2316141c8397958ec3443b0bec89496bdb9)
- Equations:
![{\displaystyle v_{2}=r_{1}*i_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cae9d9bbde110cb3c3348a72e5b0a9f0a044bcc3)
![{\displaystyle i_{3}=c_{1}{d \over dt}v_{3}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/47fec5feaa93bc187c22626ee86f29122574c4a8)
![{\displaystyle v_{9}=r_{3}*i_{6}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/663eac5ab24e6e0d42a32ac9a4b9af9c081f6f23)
![{\displaystyle v_{6}=L_{1}*{d \over dt}i_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7b17eb38fb5fe841c1fc59f3e2014dd7be20ab44)
![{\displaystyle i_{4}=c_{2}{d \over dt}v_{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c4c5afd685ae46dc1d252e43a449388c32c08644)
![{\displaystyle v_{5}=L_{2}*{d \over dt}i_{5}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f186379e049179d3021f5c324172164594eba7ba)
![{\displaystyle v_{7}=r_{2}*i_{1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f89d4a68f2a294eb1a06206cb6b41a9a9aaf8a0)
![{\displaystyle i_{2}+I_{1}-i_{3}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9e036738003d6d916a2e40c6ee632fcf97773ada)
![{\displaystyle i_{3}-I_{4}-i_{6}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b25654644abc2d0a2abdf9a5d2241b48a308b5bd)
![{\displaystyle i_{4}-i_{1}-i_{5}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6434a59f54ebc1e31b5ac5560bbe8495a034b684)
![{\displaystyle v_{1}+v_{2}+v_{3}+v_{9}+v_{6}-V_{1}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3fcbc7bb9ec7483d8368e8eb8742b48a94f585cd)
![{\displaystyle v_{4}+v_{5}-v_{9}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/069e5473442c4ccbac24f85e611b9d773bfcf5b4)
![{\displaystyle v_{7}+v_{3}+v_{4}-v_{8}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d3d9748ed0b6fe1e467b393420c828ca41dd324)
- numeric solution calculated in the phasor domain
- simulation at circuitlab