Circuit Theory/Example70

original circuit The series components can be lumped together .. which simplifies the circuit a bit. Node Analysis Node analysis thumb|mupad and matlab /code/ for all the work below Mesh Analysis Mesh analysis Solving Which is the same as the voltage through the 1 ohm resistor. Thevenin voltage Thevenin voltage requires opening the load Make ground the negative side of , then: Solving Norton Current Thevenin/Norton Impedance File:Example70impedance.png short voltage sources, open current sources, remove load and find impedance where the load was attached check yes! they match Evaluate Thevenin Equivalent Circuit File:Example70theveninEquivalent.png Going to find current through the resistor and compare with mesh current yes! they match Find Load value for maximum power transfer Find average power transfer with Load that maximizes Simulation border|800px| The circuit was simulated. A way was found to enter equations into the voltage supply parameters which improves accuracy: To compare with the results above, need to translate the current and voltage through the resistor into the time domain. Period Period looks right about 6 seconds ... should be: Current Current through 1 ohm resistor, once moved into the time domain (from the above numbers) is: From the mesh analysis, the current's through both sources were computed: The magnitudes are accurate, they are almost π out of phase which is can be seen on the simulation. Voltage The voltage is the same as the current through a 1 ohm resistor: The voltage of the first (left) source is: The magnitudes match. The voltage through the source peaks before the current because the first source sees the inductor. The voltage through the resistor should peak about 171 - 45 = 126° before the source ... which it appears to do.