Question

How does the total impedance change in a parallel RL circuit as frequency increases?

Answer 1

In a parallel RL (Resistor-Inductor) circuit, the total impedance changes as the frequency increases due to the inductive reactance of the inductor. The impedance in a parallel RL circuit is given by the reciprocal of the sum of the reciprocals of the individual impedance components (resistor and inductor). The impedance (Z) of a parallel RL circuit is given by the following formula:

1

=
1

+
1



Z
1
    ​

=
R
1
    ​

+
jωL
1
    ​


Where:


Z is the total impedance of the parallel RL circuit.

R is the resistance in ohms.

L is the inductance in henries.

ω is the angular frequency in radians per second (equal to
2

2π times the frequency in Hertz).

j is the imaginary unit (

2
=
−
1
j
2
=−1).

The term
1



jωL
1
    ​

 represents the inductive reactance (


X
L
    ​

) of the inductor, and its value is inversely proportional to the frequency (

f) or angular frequency (

ω) of the alternating current passing through the circuit.

As the frequency increases, the angular frequency

ω increases, and therefore the inductive reactance


X
L
    ​

 decreases. This results in a decrease in the overall contribution of the inductor's reactance to the total impedance. Consequently, the total impedance of the parallel RL circuit decreases as the frequency increases.

It's worth noting that the resistance (

R) component remains constant with frequency, as it is not dependent on the frequency of the AC source. So, in summary, as the frequency increases in a parallel RL circuit, the total impedance decreases due to the decrease in inductive reactance.