What is the impedance of an AC series circuit that is constructed of a 10.0-Ω resistor along with 24.0-Ω inductive reactance and 7.0-Ω capacitive reactance?
A)19.7 Ω
B)11.2 Ω
C)41.0 Ω
D)27.7 Ω

Question

Quizplus · Accepted Answer

To calculate the total impedance (Z) of the circuit, we need to add the resistive, inductive, and capacitive impedances vectorially. Mathematically,

Z^2 = R^2 + (XL - XC)^2

Where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.

Substituting the given values, we get:

Z^2 = (10)^2 + (24 - 7)^2

Z^2 = 10^2 + 17^2

Z^2 = 10^2 + 289

Z^2 = 389

Z = sqrt(389)

Z = 19.7 Ω

Therefore, the impedance of the AC series circuit is 19.7 Ω, which is closest to option A (19.7 Ω).

What Is the Impedance of an AC Series Circuit That