Determine the driving-point impedance of the network at a frequency of kHz:

# Solution

Lets first find impedance of elements one by one:

## Resistor

The resistor impedance is purely real and independent of frequency.

## Inductors and

The inductor impedance is purely imaginary and directly proportional to frequency:

We need to find the impedance in kHz. Therefore:

## Capacitor

The capacitor impedance is purely imaginary and inversely proportional to frequency:

To get the standard representation of complex numbers, we need to bring to numerator and this can be done by multiplying by :

Note how capacitor acts in this frequency. The value of impedance is less than . Compare this value to values of other components. It is almost equivalent to a short circuit!

## Equivalent Impedance

Let's replace the values in the circuit:

and are parallel.

One interesting point here is that unlike pure resistive circuits where the equivalent resistance of parallel elements is always less than the resistance of each element, the value of the equivalent impedance of parallel elements can be greater than the value of the impedance of elements. Here the capacitor impedance value is but the equivalent impedance, , is higher.

Three components are in series. Therefore:

Now, determine the impedance at Hz and kHz and share it with others below in comments section.

Determine the driving-point impedance of the network at a frequency of 2 kHz:

Zc was calculated as -j0.796 Ohms but the correct calculation is -j0.0796 ohms

The final answer will be 20+j12.52 = 23.6 with angle of 32.05.

Thanks

In solving for the impedance of the Capacitor, you use .0001 as the value for 1000uF.

The question asks for a 1000 µF (1 mF) capacitor, but the solution is made with a 100 µF (0.1 mF) capacitor.

Thank you for reminding. It is fixed now.

Thanks sir for the content you have provided which really help me to improve my concept...

Really nice to see the different steps. Thanks!

Why you didn't drop the solution