Solve the circuit by mesh analysis and find the current and the voltage across .
There are four meshes in the circuit. So, we need to assign four mesh currents. It is better to have all the mesh currents loop in the same direction (usually clockwise) to prevent errors when writing out the equations.
Determine the stability of the system whose characteristics equation is:
All coefficients are positive and non-zero; therefore, the necessary condition for stability is satisfied. Let's write the Routh array:
Determine the driving-point impedance of the network at a frequency of kHz:
Lets first find impedance of elements one by one:
The resistor impedance is purely real and independent of frequency.
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Find and :
Find using superposition rule:
The superposition theorem states that the response (voltage or current) in any branch of a linear circuit which has more than one independent source equals the algebraic sum of the responses caused by each independent source acting alone, while all other independent sources are turned off (made zero).