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Admittance of a Parallel Circuit

Let us study the parallel combination and admittance in such case. For this ,we need to consider two branches connected in parallel where one branch is series combination of Capacitive Reactance and Resistance and other branch is Series combination of inductance and resistance

Parallel Circuit

We will individually analyse the two branches first

For branch A, from previous derived results

Conductance G1=R1/(R12+XL2)= R1/Z12

Here Z1 is impedance in ohms

Inductive susceptance BL=XL/(R12+XL2)=XL/Z12

Then Y1=G1-jBL= R1/Z12 – jXL/Z12

Similarly for branch B

Conductance G2=R2/(R22+Xc2)= R2/Z22

Here Z2 is impedance in ohms

Inductive susceptance

Bc=Xc/(R22+Xc2)=Xc/Z22

Then Y2=G2+jBc= R2/Z22 + jXc/Z22

On adding the two admittance in series (parallel admittance is added like series)

Y=Y1+Y2

Then Y=G1-jBL+ G2-jBC

∴ Y=(G1+G2)-J(BL+BC)

Finally ,Y=(R1/Z12+R2/Z22) -j(XL/Z12-XC/Z22)

This is how we can obtain admittance of the whole circuit.

Admittance

In general, when talking about electrical circuits we only refer to certain properties like voltage developed and resistance offered by circuit. Resistance can be defined as the opposition offered by the electrical circuit for current to flow. In this article, we will introduce a new property known as the admittance of the circuit. It is often taken into account when we want to know how easily the circuit allows current to flow through it. It is basically a term contrary to resistance. In this article, we will discuss what is admittance along with its derivation from the impedance. We will also learn about the admittance triangle and how admittance varies in series and parallel combination circuits. We will also list the components of admittance and provide a comparison between admittance and impedance. This information when put to use can be applied at various places which have been discussed through the applications. We will conclude the article with some points and list some frequently asked questions for reference.

Table of Content

  • Derivation
  • Components
  • Admittance Triangle
  • Admittance of a Series Circuit
  • Admittance of a Parallel Circuit
  • Admittance Vs Impedance
  • Applications
  • Solved Examples

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What is Admittance?

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Admittance Triangle

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Admittance of a Series Circuit

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Admittance of a Parallel Circuit

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Conclusion

As we have seen that admittance i.e. the reciprocal of impedance is an important quantity used for analysing and designing circuits. The magnitude and phase of impedance are used for determining some important quantities like power reflected in circuits. We have also seen that there are various methods used for calculating the admittance of the circuit depending on whether it is a series or a parallel circuit. We have also seen the difference between admittance and reactance through a tabular format and also analysed the applications of admittance in real-life....

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