# Why inductive reactance has two formulas

We know inductive reactance XL will have two formulas. One is XL = 2piFL and other is XL = V/I (Ohm's law). Why we have 2 formulas for inductive reactance.

Is the solution ( inductive reactance value) obtained from these two formulas will be going to be same or different ?

• We also have two formulas for number 2. It's 1+1 and 3-2. Of course these are the same (assuming V and I are the effective DC-equivalent of the actual AC values..)! – Eugene Sh. Apr 25 '18 at 18:27
• 3-2???????????? – Oldfart Apr 25 '18 at 18:36
• :-D I thought 3-1 – Meenie Leis Apr 25 '18 at 18:37
• Hm. Sorry. Just got my coffee. Damn.. Totally ruined my point :D – Eugene Sh. Apr 25 '18 at 19:28
• You don't need such precision in every day engineering. – Gregory Kornblum Apr 25 '18 at 20:54

Well if you can find $c$ using $a+b = c$ or by using $e+f = c$, then $a + b$ should have to be equal to $e + f$

One is XL = 2piFL and other is XL = V/I (Ohm's law). Why we have 2 formulas for inductive reactance.

We don't. An inductor's impedance has two components. One (ohmic) is independent of frequency. The other (inductive) is proportional to frequency. The two components behave differently, so each has a different formula. And only the second formula describes inductive reactance. The first, although part of any real inductor (except for superconductors), is not, properly speaking, inductive.

And you should keep in mind that, while we're on the subject of "real" components, that real inductors also have a capacitive term. This will affect any inductor used in a resonant circuit, since resonance frequency will be affected by the intrinsic capacitance.

There's this formula for inductance: -

L = Voltage divided by rate of change of current = $\dfrac{V\cdot dt}{di}$

And that formula spins off the formula for AC reactance and, by definition of what ohms law is, the voltage/current formula.

So, realistically, there's only one formula for inductance because every other formula is derived from it. An inductor does what it says on the tin and that tin is: -

$V = L\dfrac{di}{dt}$ - it works every time.