Question

An RL circuit consists of a 40.0 Ω resistor and a 3.00 mH inductor. Find its impedance Z at 60.0 Hz and 10.0 kHz.

a) 40.1 Ω, 403.6 Ω
b) 40.2 Ω, 402.5 Ω
c) 40.3 Ω, 401.4 Ω
d) 40.4 Ω, 400.3 Ω

Answer 1

The impedance of an RL circuit can be calculated using the formula Z = √(R² + (Xl - Xc)²). At 60.0 Hz, the impedance is 40.1 Ω and at 10.0 kHz, the impedance is 403.6 Ω.

Step-by-step explanation:

The impedance of an RL circuit can be calculated by using the formula: Z = √(R² + (Xl - Xc)²), where Z represents impedance, R represents resistance, Xl represents inductive reactance, and Xc represents capacitive reactance.

At 60.0 Hz, the impedance of the RL circuit can be calculated as follows:

Z = √(40.0² + (2πfL - 1/(2πfC))²)

Z = 40.1 Ω

At 10.0 kHz, the impedance of the RL circuit can be calculated as follows:

Z = √(40.0² + (2πfL - 1/(2πfC))²)

Z = 403.6 Ω

Therefore, the impedance of the RL circuit at 60.0 Hz is 40.1 Ω, and at 10.0 kHz is 403.6 Ω. The correct answer is (a) 40.1 Ω, 403.6 Ω.