Admittance of resistance and inductor [AC circuit]

antiantianti

Joined Aug 4, 2016
45
Hi
My problem is to compute the admittance of a resistor in parallel with an inductor online i saw that
1/Z=sqrt((1/R)^2+(1/2*pi*f*L)^2)
but in a book i saw 1/Z=(1/R)+(1/(2*pi*f*L*j))
what is the relationship between the two My idea is that the first is only the magnitude . The second are vectors instead of only the magnitude but can anyone prove the second

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LesJones

Joined Jan 8, 2017
4,220
The first equation is just applying Pythagoras's theorem to the second equation. (In the second equation "j" denotes that the second term of the equation is at right angles to the first term so you need Pythagoras's theorem to add the two terms.)

Les.

MrAl

Joined Jun 17, 2014
11,595
Hi
My problem is to compute the admittance of a resistor in parallel with an inductor online i saw that
1/Z=sqrt((1/R)^2+(1/2*pi*f*L)^2)
but in a book i saw 1/Z=(1/R)+(1/(2*pi*f*L*j))
what is the relationship between the two My idea is that the first is only the magnitude . The second are vectors instead of only the magnitude but can anyone prove the second
Hi,

The second formula is the true admittance, which is the complex admittance.
Formally, the first formula is the magnitude of the admittance which may also be referred to as the admittance informally.
Because the first formula is really just the magnitude, that would mean some problems would require an associated angle to go with that magnitude as a complex quantity can only be described completely by specifying two values not just one.

So we have two forms here:
1. magnitude, phase angle
2. real part+i*imaginary part

The first formula specifies the first part of #1 above while the second formula specifies #2 completely.