# The Difference Explained Between: Impedance (Z), resistance (R), reactance (X), inductive reactance (XL), inductance (L), capacitive reactance (XC), c



## Zach Stone P.E.

This is part of a blog post originally posted on our free articles section at www.electricalpereview.com

You can read the entire article here in the original formatting: Free Articles: Impedance, Reactance, Admittance, Susceptance - Whats the difference?

This will be a great resource for anyone who has had any lingering questions with any of these terms.  

Know that the most commonly confused terms are inductive reactance [[COLOR= rgb(51, 51, 51)]Ω][/COLOR] vs inductance [L], and capacitive reactance [[COLOR= rgb(51, 51, 51)]Ω][/COLOR] vs capacitance [F].

Feel free to print this out and add it to your references for the Electrical PE Exam. 


The many “-tance” terms of Electrical Engineering




There are *many different types of impedance components* and they all rhyme, making it hard to remember which one is which.

Many even have the same units, which can lead to even further confusion.

Don’t let the same *“-tance” ending* fool you.

If you run into a question on the Electrical PE Exam that asks to solve for one of these components and you aren’t familiar with the exact differences, then *you could end up bubbling the wrong answer* even if your math and calculations are sound.

Chances are, you’ve already run into a similar mistake or headache while working sample exam practice problems.

*To make sure this doesn’t happen on the exam day*, let’s take a look at all the different components and define them, as well as understand where each comes from.


First


We’ll start with *impedance (Z)*, a complex number, and take a closer look at both its real and imaginary components *resistance (R) *and *reactance (X).*


Second


We’ll deep dive a little further into both types of reactances, *inductive reactance** (XL**) *and *capacitive reactance (XC).*


Third


We will explore *admittance (Y)*, another complex number, and take a closer look at both of its real and imaginary components *conductance (G)* and *susceptance (B)*.


Impedance (Z)


Impedance is best described as the total *opposition of the flow of current* through a circuit when voltage is applied. Impedance is a *complex number* with both a real and imaginary component, it is represented by the *capital letter Z*, and has the unit of *ohms [Ω].*

Written in *complex rectangular form*, impedance looks like this:







Impedance is the *sum of resistance (R) and reactance (X).*

Resistance is the *real component of impedance, or Re{Z}* and reactance is the *imaginary component of impedance, or Img{Z}.*

Impedance is typically represented in a circuit as either a block component:






A resistive component with a positive inductive reactance:






Or a resistive component with a negative capacitive reactance:






Impedance is most often calculated by *re-writing ohm’s law to solve for Z:*






Further recommended reading: *https://en.wikipedia.org/wiki/Electrical_impedance*


Resistance (R)


Like impedance, resistance also *opposes the flow of current* when voltage is applied. A purely resistive impedance lacks a reactive impedance component, such as a *heating element, radiator, or a resistor.*

Resistance is represented by the *capital letter R*, it is the *real component of impedance Re{Z}*, and therefore not a complex number, and the *unit is ohms [Ω].*

A resistance impedance component is represented in a circuit as a resistor:






Further recommended reading:  *https://en.wikipedia.org/wiki/Electrical_resistance_and_conductance*


Reactance (X)


There are two types of reactance. Reactance will either *oppose the change of current or voltage* depending on which of the two types it is.

*Inductive* *reactance* will *oppose the change of current.*






*Capacitive* *reactance* will *oppose the change of voltage.*

*



*

Reactance is represented by the *capital letter X*, it is the *imaginary component of impedance Img{Z}*, and therefore not a complex number, and the *unit is ohms [Ω].*

Further recommended reading:* https://en.wikipedia.org/wiki/Electrical_reactance*


Inductive Reactance (XL) and Inductance (L)


Inductive reactance is one of two types of reactance, and is an imaginary impedance component that *opposes the change of current*. It is represented by the *capital letter X with an L subscript* and also has the *unit of ohms [Ω].*

*Inductive reactance* in ohms comes from angular frequency in radians per second, times inductance per unit length, times the total length of the component:






Where *inductance is measured in total Henrys [H]*:






And *ω, the angular frequency in radians per second* is found by multiplying the 2π times frequency:






In a circuit diagram, *inductive reactance* is typically *represented by a coil*, since inductors are typically made by coiling a conductor into the shape of a solenoid.

Inductive reactance will always be a *positive imaginary impedance component,* or* +jX.*






*inductive reactance* resists the flow of current by the *magnetic flux that builds around it.*

An example of an *inductive reactance* would be a perfect ideal coil, like the *windings in a motor or generator* stator.

Further recommended reading: *https://en.wikipedia.org/wiki/Inductance*

Further recommended reading: *https://en.wikipedia.org/wiki/Henry_(unit)*


 



Capacitive Reactance (XC) and Capacitance (C)


Capacitive reactance is one of two types of reactance, and is an imaginary impedance component that *opposes the change of voltage.* It is represented by the *capital letter X with a C subscript* and also has the *unit of ohms [Ω].*

*Capacitive reactance* in ohms comes from the inverse of the angular frequency in radians per second, times capacitance per unit length, times the total length of the component:






Where *capacitance is measured in total Farads [F]*:






And *ω, the angular frequency in radians per second* is found by multiplying the 2π times frequency:






In a circuit diagram, a capacitive reactance is typically *represented by the capacitor symbol*, since capacitors are typically made up of two conducting plates that are separated by a dielectric medium.

Capacitive reactance resists the flow of voltage by the the *buildup of charge between two conducting plates.*

Capacitive reactance will always be a negative *imaginary impedance component*, or *-jX.*

*



*

An example of a purely capacitive reactance would be a *perfect idea capacitor.*

Further recommended reading: *https://en.wikipedia.org/wiki/Capacitance*

Further recommended reading: *https://en.wikipedia.org/wiki/Farad*


Admittance (Y)


Admittance is the *opposite of impedance* and as such, is best described as* how easy a current can flow* when voltage is applied, *or how much current is **admitted* through the circuit. If impedance is more akin to current friction, than admittance would be comparable to ice or a slippery surface. Admittance is represented by *the capital letter Y*, and has the *unit of siemens (S)*, and is *a complex number.*

Impedance is a *complex number* because it has both a real and imaginary value.

Written in *complex rectangular form*, admittance looks like this:






It is the *sum of conductance (G) and susceptance (B).*

Conductance is the real component of admittance Re{Y} and susceptance is the imaginary component of admittance Img{Y}.

Impedance is most often calculated by taking the *inverse of impedance:*






*Ohm’s law* can also be rewritten to use admittance instead of impedance to *solve for both voltage and current:*






Impedance is most often represented by its admittance antinome when an impedance component is placed in a circuit such that it creates a *shunt (parallel) least resistance path to ground, neutral, or another phase.*

Since more current will flow through a path of least resistance (I=V/R), a shunt connection with a very small impedance means that the *majority of current entering a shared node will flow through it* rather than any other path.

Further recommended reading:* https://en.wikipedia.org/wiki/Admittance*


Conductance (G)


Conductance is the *opposite of resistance*, it is the real *component of admittance Re{Y}* and therefore not a complex number, it is represented by the *capital letter G*, and has the *units of siemens (S).*

Conductance is found by taking the *inverse of resistance:*






If resistance is the opposition of current, then conductance is *how easily current can flow* similar to our analogy of ice or a slippery surface compared to friction.

An easy way to remember the definition of conductance is by relating it to *how well a circuit will conduct current.*

Further recommended reading: *https://en.wikipedia.org/wiki/Electrical_resistance_and_conductance*


Susceptance (B)


Susceptance is the *opposite of reactance,* it is the *imaginary component of admittance Img{Y}* and therefore not a complex number, it is represented by the *capital letter B*, and has the *units of siemens (S).*

Susceptance is found by taking the *inverse of reactance:*






If reactance opposes the change of current or voltage, than *susceptance is the quality of how easily current or voltage can change in a circuit.*

An easy way to remember the definition of susceptance is by relating it to *how susceptible a circuit is to the change of current or voltage.*

Further recommended reading: *https://en.wikipedia.org/wiki/Susceptance*


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## Zach Stone P.E.




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## apprentice

Electrical PE Review said:


> Conductance is the *opposite of inductance*


I think the writer meant to say resistance and not inductance!


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## P-E

At first I thought this might be about shirt sizes.


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