Complex 2R, L, C, voltage circuit
Given that the voltage source is defined by
and the current source is defined by
, find all other voltages, currents and check power.
Circuit marked up for analysis
- Knowns:
![{\displaystyle V_{s},R_{1},R_{2},L,C,I_{s}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3cf5f88ca4e93205ffc94f575c5e1e2a2b441354)
- Unknowns:
![{\displaystyle v_{1},v_{2},v_{C},v_{L},i_{1},i_{2},i_{C},i_{L}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e8c5227fa59102e23be6e1fe78678ee99b689de4)
- Equations:
![{\displaystyle v_{1}=R_{1}*i_{1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ea0c86f8408d95e30fac2845ffb65eaf96c56e05)
![{\displaystyle v_{2}=R_{2}*i_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2cb4897331be52ff90f5d15273a181f3dc42ebc1)
![{\displaystyle i_{C}=C*{d \over dt}v_{C}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a79c659533d1169032b0f5c486a70905cce4c8d6)
![{\displaystyle v_{L}=L*{d \over dt}i_{L}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/31323ecae589cd2336b5ad27fd90349ce0e455f5)
![{\displaystyle i_{1}+I_{s}-i_{2}-i_{C}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/784427410e2e192b4acc4e54df75a3b020f0dd40)
![{\displaystyle i_{c}-I_{s}-i_{L}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1296630fbd856a26ba274d2700a95e92b850b174)
![{\displaystyle v_{1}+v_{2}-V_{s}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a4b165cb24dd528daa1e0d331c09a7b20c50089)
![{\displaystyle v_{C}+v_{L}-v_{2}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/19d2dc9fe6b48a31c4e7618056520f6a29234385)
- numeric solution calculated in the phasor domain
- attempt at a Laplace solution
- simulation at circuitlab