### Video Transcript

Which of the following formulas
correctly relates the reactance π of an inductor to its inductance πΏ when
connected to an alternating-voltage source with a frequency π? (A) π equals one over two ππ
times πΏ. (B) π equals πΏ over two ππ. (C) π equals two ππ times
πΏ. (D) π equals two π π over
πΏ. And (E) π equals two ππΏ over
π.

Weβre looking here for the correct
formula for the reactance of an inductor. Letβs say that this is our inductor
and itβs connected, weβre told, to an alternating-voltage source. Reactance is a term we often
encounter when weβre working with alternating-voltage circuits. Reactance is like resistance. Itβs the measure of a given
componentβs opposition to the flow of charge. In our circuit then, which has an
inductor of inductance πΏ and is operating at a frequency π, we want to write an
equation for how much this inductor opposes charge flow. Thatβs its reactance. To begin figuring out which of our
answer options is correct, letβs imagine what will happen as πΏ and π in the
circuit are varied.

First, letβs think about changing
the frequency π. We know that a general property of
inductors is that they resist changes to current through them. This means that if we increase π,
the frequency at which voltage as well as current oscillates in the circuit, then
that will also lead to an increase in the opposition of the inductor to the flow of
charge. In other words, increasing π will
make the inductorβs reactance π go up. Knowing this, we can now eliminate
any answer options where reactance π and frequency π are inversely related. We see such an inverse relationship
in answer option (A) as well as answer option (B) and answer option (E). All of these choices claim that,
for example, if π increased, then π, the reactance, would decrease. We know thatβs not true though. So weβll cross out these answer
choices.

Next, letβs imagine in our circuit
what will happen if the inductance πΏ of the inductor goes up. In this case, the inductorβs
capacity for opposing changes in current will be increased, therefore, so will its
capacity to oppose the flow of charge. Its reactance will increase as
inductance increases. This means we can eliminate any
answer options where π, the reactance, and πΏ, the inductance, are inversely
related. We see that answer choice (D)
claims that they are. This though would mean that as
inductance increases, reactance decreases. And we know that thatβs not the
case.

This leaves us with answer choice
(C). This choice says that reactance is
directly proportional to frequency as well as inductance. We found this to be an accurate
description of what happens physically in an alternating-current circuit with an
inductor. Inductive reactance equals two
times π times π times πΏ. And just as a side note, the
reactance of an inductor is often represented π sub L. This lets us know specifically
which circuit component weβre considering. In any case, in answer to this
question, we choose option (C).