- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Resistance and Impedance in an AC Circuit

## Resistance in an AC Circuit

Consider the circuit diagram, containing an AC sinusoidal voltage source and an unknown passive element (K). The element K will be a *resistance*, only if the voltage across it and the current flowing through it, are in phase with each other.

### Explanation

Let the equation for alternating voltage is

$$\mathrm{v=V_{m}\sin\omega\:t\:\:\:...(1)}$$

As a result of this voltage, an alternating current i will flow through the element. Now, the applied voltage has to overcome the drop in the element only, i.e.

$$\mathrm{v=i\times\:k}$$

$$\mathrm{\Rightarrow\:i=\frac{v}{k}=\frac{V_{m}\sin\omega\:t}{k}\:\:\:...(2)}$$

The value of current will be maximum, when *sin(ωt) = 1*.

$$\mathrm{\therefore\:I_{m}=\frac{V_{m}}{K}}$$

Thus, the equation (2) becomes,

$$\mathrm{i=I_{m}\sin\omega\:t\:\:\:...(3)}$$

It is clear from the eqns. (1) and (3) that the applied voltage and resulting current are in phase with each other. Therefore, the unknown element is resistance, i.e.

$$\mathrm{K=R\:\:\:...(4)}$$

## Impedance in an AC Circuit

If an AC circuit containing both resistive and reactive components, then the total opposition offered by the circuit in the flow of electric current is known as *impedance of the AC circuit.*

It is denoted by letter ‘Z’ and measured in ohms (Ω).

Mathematically, the impedance is expressed as,

$$\mathrm{Impedance,Z=R+jX\:\:\:...(5)}$$

**Case 1 – Impedance of a Series R-L Circuit**

$$\mathrm{Z=R+jX_{L}=R+j\omega\:L\:\:\:...(6)}$$

**Case 2 – Impedance of a Series R-C Circuit**

$$\mathrm{Z=R+jX_{C}=R-j\frac{1}{\omega\:C}\:\:\:...(7)}$$

**Case 3 – Impedance of a Series RLC Circuit**

$$\mathrm{Z=R+j(X_{L}-X_{C})=R+j(\omega\:L-\frac{1}{\omega\:C})\:\:\:...(8)}$$

**Case 4 – Impedance in a Parallel AC Circuit**

In case of a parallel AC circuit, the impedance being given in terms of *admittance,* i.e.

$$\mathrm{Impdance=\frac{1}{Admittance}}$$

$$\mathrm{\Rightarrow\:Z=\frac{1}{Y}=\frac{1}{G+jB}\:\:\:....(9)}$$

Where,

**G**= 1/R, is called conductance**B**= 1/X, is called susceptance

- Related Articles
- Reactance and Impedance
- An electric lamp of resistance 20 Ω and a conductor of resistance 4 Ω are connected to a 6 V battery as shown in the circuit. Calculate:(a) the total resistance of the circuit\n
- How to Calculate Equivalent Resistance (Series & Parallel Circuit Examples)
- Power in AC Circuit – Active Power, Reactive Power, Apparent Power
- Equivalent Circuit of an Induction Motor, Stator Circuit Model and Rotor Circuit Model
- What is Electrical Impedance?
- Difference between an Inverter AC and a Non-Inverter AC
- Draw circuit symbols for a) fixed-resistance b) variable resistance c) a cell d) a battery of 3 cells e) an open switch f) a closed switch
- What is Synchronous Reactance & Synchronous Impedance?
- Find the equivalent resistance, REQ between A-B for the following resistor combination circuit."\n
- What is a circuit diagram? Draw the labelled diagram of an electric circuit comprising of a cell, a resistor, an ammeter, a voltmeter and a closed switch(or closed plug key). Which of the two has a large resistance: an ammeter or a voltmeter?
- Magnetic Circuit – Series and Parallel Magnetic Circuit
- Difference between Electric Circuit and Magnetic Circuit
- Difference between Open Circuit and Closed Circuit
- Difference between Open Circuit and Short Circuit