### Video Transcript

Which of the following formulas
correctly relates the impedance π of a circuit to the circuitβs capacitive
reactance π sub πΆ, the circuitβs inductive reactance π sub πΏ, and the circuitβs
resistance π
?

Each of our five answer options
purports to give the correct equation for the impedance of a circuit π. Impedance, we can recall, is an
overall measure of the opposition to the flow of charge in a circuit. Itβs a term that applies for
alternating current circuits. And it accounts for, we could say
βsums up,β the total resistance and reactance of all components in the circuit.

Knowing that, we might think that
the impedance π of a circuit simply equals the sum of π sub πΆ, π sub πΏ, and
π
. Note, however, that every single
one of our equations has a square root, thatβs what this one-half power effectively
means, and that the terms inside the parentheses for each answer option are
squared.

We might be drawn then to answer
option (D), where we see that π is claimed to be equal to the square root of π
squared plus π πΏ squared plus π πΆ squared. In fact, though, this is not the
correct equation for impedance. The correct equation for impedance
involves a subtraction. We take the capacitive reactance of
a circuit, and we subtract it from the inductive reactance. The correct equation for π will
involve a term that looks like this

Notice this means that answer
option (B) is also eliminated. Here, we donβt subtract π sub πΆ
from π sub πΏ. In answer options (A), (C), and
(E), there is a subtraction. But in choice (A), this subtraction
is an π sub πΏ term from an π sub πΆ term. We know that order is reversed, so
(A) canβt be correct. And then in option (C), we do have
π sub πΆ being subtracted from π sub πΏ, but these terms are both squared. The correct equation for impedance
π, though, has a term where π sub πΆ to the first power, we could say, is
subtracted from π sub πΏ to the first power.

The correct formula is given by
option (E), impedance π equals the square root of π
squared plus the quantity π
sub πΏ minus π sub πΆ squared.