Single Phase AC Circuits

# Components of Admittance. ( Simple Explanation)

**Components of Admittance.**

**Conductance:**

A component of admittance inphase with the applied voltage is called conductance. Or the X component of admittance is called conductance. It’s represented by G and the unit of conductance is Mho or Siemens.

G = Y Cos φ = (1/Z) * (R/Z) = R/Z

^{2}= R/ (R^{2}+ X^{2})(Since Cos φ = R/Z and Y = 1/Z)

And Total Conductance G

_{T }= G_{1}+G_{2}+G_{3+…..}**Susceptance:**

That component of admittance, which has an angle of 90 degree with applied voltage is called suserptance. ..or Y component of admittance is celled susceptnce, its represented by B. and the unit of susceptance is also Mho or Siemens.

OR

A Component of admittance in quadrature ( at 90 degree) with the applied Voltage is called susceptance.

B = Y Sin Φ = 1/Z * X/Z = X/Z

^{2 }= X/ (R^{2 }+ X^{2}) ——–> (Since Sine Φ = X/Z)And total Susceptance = B

_{T}= B_{1}+ B_{2}+ B_{3}+…B_{n}Also Note that inductive suseptance of a circuit is negative (-), while Capacitive Susceptance of a circuit is always positive (+).

Y = G – j B

_{L}…… (In case of inductive Circuit)Y = G + B

_{C }……. (In case of capacitive circuit)For More explanation, consider the following circuit, (fig 1)

The Total conductance = algebraic sum of the conductance in each branch.

The Total conductance =G

_{T}= G_{1}+G_{2}+G_{3}Similarly,

Total susceptance = algebraic sum of the susceptance in each branch,

Total susceptance B

_{T}= (-B_{1}) + (-B_{2}) + (B_{3}).And total circuit admittance,

Y

_{T}= √ (G_{T}^{2}+ B_{T}^{2})In case of inductive Circuit Y

_{T}= √ (G^{2}+ B_{L}^{2}) and Phase angle φ tan^{-1}(-B_{L}/G)In Case of Capacitive Circuit Y

_{T}= √ (G^{2}+ B_{L}^{2}) and phase angle φ tan^{-1}(B_{c }/G)And Total current, I = VY,