A 200-Ω resistor, a 40.0-mH inductor and a 2.00-μF capacitor are connected in series with a 120-V rms source at 1000 Hz. What is the impedance of this circuit?
A) 164 Ω
B) 120 Ω
C) 264 Ω
D) 200 Ω
E) 364 Ω

Question

Quizplus · Accepted Answer

The impedance of the series RLC circuit can be calculated using the formula:

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

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

We can calculate XL and XC as follows:

XL = 2πfL = 2π(1000)(0.04) = 25.13 Ω

XC = 1/(2πfC) = 1/(2π(1000)(2X10^-6)) = 79.58 Ω

Plugging in the values, we get:

Z = sqrt((200^2 + (25.13 - 79.58)^2)) = 264 Ω

Therefore, the impedance of the circuit is 264 Ω.

A 200-Ω Resistor, a 40