Question

A.C. Fundamentals - Admittance (Y) in R-L series circuit

Answer 1

In an A.C. (alternating current) electrical circuit, admittance (Y) is a measure of how easily current flows through the circuit. It is the reciprocal of impedance (Z) and is analogous to conductance in a direct current (DC) circuit.

For an R-L series circuit, which consists of a resistor (R) and an inductor (L) connected in series, the admittance (Y) can be calculated as follows:


=
1

=
1

2
+
(


−


)
2
Y=
Z
1
    ​

=
R
2
+(X
L
    ​

−X
C
    ​

)
2
    ​

1
    ​


Where:


Y is the admittance of the circuit (in Siemens, S).

Z is the impedance of the circuit (in Ohms, Ω).

R is the resistance of the resistor (in Ohms, Ω).


X
L
    ​

 is the inductive reactance (in Ohms, Ω) given by


=
2



X
L
    ​

=2πfL, where

f is the frequency of the AC signal and

L is the inductance of the inductor (in Henrys, H).


X
C
    ​

 is the capacitive reactance (in Ohms, Ω) given by


=
1
2



X
C
    ​

=
2πfC
1
    ​

, where

f is the frequency of the AC signal and

C is the capacitance of the capacitor (in Farads, F).

Admittance is a complex quantity and consists of both magnitude and phase angle components. The phase angle indicates the phase relationship between current and voltage in the circuit. The magnitude of admittance is inversely proportional to the impedance, so a lower impedance corresponds to a higher admittance and vice versa.

It's important to note that in an R-L series circuit, the presence of both resistance and inductance will affect the overall impedance and admittance of the circuit, leading to a phase shift between the current and voltage. The admittance will also depend on the frequency of the AC signal and the values of resistance, inductance, and capacitance in the circuit.