Question

An LC circuit consists of a 3.00mH inductor and a 5.00μF capacitor. Find its impedance at 60.0 Hz and 10.0 kHz.

a. 4.51 Ω at 60.0 Hz
b. 90.5 Ω at 60.0 Hz
c. 9.05 Ω at 10.0 kHz
d. 45.1 Ω at 10.0 kHz

Answer 1

The impedance (Z) of the LC circuit at 60.0 Hz is approximately 530 ohms, while at 10.0 kHz it is about 185.3 ohms. These calculations are made by finding the difference between inductive reactance (XL) and capacitive reactance (XC) at each frequency.

Step-by-step explanation:

To find the impedance of an LC circuit at different frequencies, we need to calculate the inductive reactance (XL) and the capacitive reactance (XC), then use their difference to find the total impedance (Z).

Firstly, the inductive reactance is given by XL = 2πfL, where f is the frequency and L is the inductance. The capacitive reactance is given by XC = 1 / (2πfC), where C is the capacitance.

At 60.0 Hz:

• XL = 2π(60.0 Hz)(3.00 mH) = 2π(60.0)(0.003) Ω ≈ 1.13 Ω
• XC = 1 / (2π(60.0 Hz)(5.00 μF)) = 1 / (2π(60.0)(5.00 × 10-6)) Ω ≈ 531 Ω
• Z = |XL - XC| = |1.13 Ω - 531 Ω| ≈ 530 Ω (approximately 531 Ω)

At 10.0 kHz:

• XL = 2π(10.0 × 103 Hz)(3.00 mH) = 2π(10.0 × 103)(0.003) Ω ≈ 188.5 Ω
• XC = 1 / (2π(10.0 × 103 Hz)(5.00 μF)) = 1 / (2π(10.0 × 103)(5.00 × 10-6)) Ω ≈ 3.18 Ω
• Z = |XL - XC| = |188.5 Ω - 3.18 Ω| ≈ 185.3 Ω