Circuit Theory/Example70

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original circuit

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

Node Analysis[edit]

Node analysis

mupad and matlab code for all the work below

Mesh Analysis[edit]

Mesh analysis


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

Thevenin voltage[edit]

Thevenin voltage requires opening the load

Make ground the negative side of , then:


Norton Current[edit]

Thevenin/Norton Impedance[edit]


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


yes! they match

Evaluate Thevenin Equivalent Circuit[edit]


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

yes! they match

Find Load value for maximum power transfer[edit]

Find average power transfer with Load that maximizes[edit]



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.