Circuit Theory/Example70
The series components can be lumped together .. which simplifies the circuit a bit.
Node Analysis
[edit  edit source]Mesh Analysis
[edit  edit source]Solving
Which is the same as the voltage through the 1 ohm resistor.
Thevenin voltage
[edit  edit source]Make ground the negative side of , then:
Solving
Norton Current
[edit  edit source]
short out the load

split into two circuits so can use superposition

half the circuit is shorted out by shorting the voltage sources
Thevenin/Norton Impedance
[edit  edit source]short voltage sources, open current sources, remove load and find impedance where the load was attached
check
yes! they match
Evaluate Thevenin Equivalent Circuit
[edit  edit source]Going to find current through the resistor and compare with mesh current
yes! they match
Find Load value for maximum power transfer
[edit  edit source]Find average power transfer with Load that maximizes
[edit  edit source]Simulation
[edit  edit source]The circuit was simulated. A way was found to enter equations into the voltage supply parameters which improves accuracy:

type sqrt(3) instead of a numeric approximation

added pi/2 to convert from cos to sin sources
To compare with the results above, need to translate the current and voltage through the resistor into the time domain.
Period
[edit  edit source]Period looks right about 6 seconds ... should be:
Current
[edit  edit source]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
[edit  edit source]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.