Question

For an RLC series circuit with a 1.00 kΩ resistor, 150 μH inductor, and 25.0 nF capacitor, calculate the circuit’s impedance at 500 Hz.

a) 2.65 kΩ
b) 1.92 kΩ
c) 3.08 kΩ
d) 2.21 kΩ

Answer 1

The impedance of the RLC series circuit at 500 Hz is 1.92 kΩ .Therefore, the correct answer is option b) 1.92 kΩ

Step-by-step explanation:

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

Z = sqrt[(R^2) + ((wL - 1/(wC))^2)]

where Z is the impedance, R is the resistance, w is the angular frequency (2πf), L is the inductance, and C is the capacitance.

For the given circuit at 500 Hz, we have:

R = 1.00 kΩ = 1000 Ω

L = 150 μH = 150 x 10^-6 H

C = 25.0 nF = 25 x 10^-9 F

Substituting these values into the formula, we get:

Z = sqrt[(1000^2) + ((2π x 500 x 150 x 10^-6 - 1/(2π x 500 x 25 x 10^-9))^2)]

Z = 1.92 kΩ

Therefore, the correct answer is option b) 1.92 kΩ