How do you calculate admittance in a resistor, inductor, and capacitor?

The impedance of a circuit element can be represented in complex form as Z = R + jX, where R is the resistance (in ohms), X is the reactance (in ohms), and j is the imaginary unit (√(-1)).

For each circuit element:

Admittance in a Resistor (Yr):

In a resistor, the reactance (X) is zero since resistors only have resistance (R). Therefore, the impedance Z = R + j(0) = R. The admittance is simply the reciprocal of the impedance: Yr = 1/R.

Admittance in an Inductor (Yl):

In an inductor, the reactance (X) is given by Xl = 2πfL, where f is the frequency of the AC signal (in Hz) and L is the inductance of the inductor (in henrys). The impedance Z = R + jXl. The admittance is the reciprocal of the impedance: Yl = 1/(R + jXl).

Admittance in a Capacitor (Yc):

In a capacitor, the reactance (X) is given by Xc = 1/(2πfC), where f is the frequency of the AC signal (in Hz) and C is the capacitance of the capacitor (in farads). The impedance Z = R + jXc. The admittance is the reciprocal of the impedance: Yc = 1/(R + jXc).

Please note that the admittance is a complex quantity, and it consists of a real part (conductance) and an imaginary part (susceptance). The conductance (G) represents the real part of the admittance and is measured in siemens (S), while the susceptance (B) represents the imaginary part of the admittance and is also measured in siemens (S). The conductance and susceptance are related to the resistance and reactance as follows:

G = Re(Y) (Real part of admittance)

B = Im(Y) (Imaginary part of admittance)

If you need to calculate the admittance of a specific circuit, you'll have to determine the values of resistance, inductance, and capacitance for the elements involved and apply the appropriate formulas mentioned above.