Determine Z in polar form for f = 7 kHz and draw a graph of impedance vs. frequency using...

Determine Z in polar form for f = 7 kHz and draw a graph of impedance vs. frequency using the values in this example.

Example

For each of the following input frequencies, find the impedance in polar form for the circuit in Figure. Note the change in magnitude and phase angle with frequency.

Figure

Solution

(a) At f = 1 kHz,

The circuit is clearly capacitive, and the impedance is

The negative sign for the angle is used to indicate that the circuit is capacitive.

(b) At f = 2kHz,

The circuit is still capacitive, and the impedance is

(c) At f = 3.5kHz,

The circuit is very close to being purely resistive because XC and XL are nearly equal, but it is slightly inductive. The impedance is

(d) At f = 5kHz,

The circuit is now predominantly inductive. The impedance is

Notice how the circuit changed from capacitive to inductive as the frequency increased. The phase condition changed from the current leading to the current lagging as indicated by the sign of the angle. Note that the impedance magnitude decreased to a minimum equal to the resistance and then began increasing again. Also, notice that the negative phase angle decreased as the frequency increased and the angle became positive when the circuit became inductive and then increased with increasing frequency.