Circuit Theory/Example70

original circuit

The series components can be lumped together .. which simplifies the circuit a bit.

Node AnalysisEdit


mupad and matlab code for all the work below

Mesh AnalysisEdit





Which is the same as the voltage through the 1 ohm resistor.

Thevenin voltageEdit


Make ground the negative side of  , then:




Norton CurrentEdit


Thevenin/Norton ImpedanceEdit


short voltage sources, open current sources, remove load and find impedance where the load was attached




yes! they match

Evaluate Thevenin Equivalent CircuitEdit


Going to find current through the resistor and compare with mesh current


yes! they match

Find Load value for maximum power transferEdit


Find average power transfer with Load that maximizesEdit




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 looks right about 6 seconds ... should be:



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.


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.