Question

An RLC series circuit has a 2.6 Ω resistor, a 95 μH inductor, and a 87.5 μF capacitor.

a. Find the circuit’s impedance, in ohms, at 110 Hz.

b. Find the circuit’s impedance, in ohms, at 4.5 kHz.

c. If the voltage source supplies an rms voltage of 5.52 V, what is the circuit’s rms current, in amperes, at a frequency of 110 Hz?

d. If the voltage source supplies an rms voltage of 5.52 V, what is the circuit’s rms current, in amperes, at a frequency of 4.5 kHz?

e. What is the resonant frequency, in kilohertz, of the circuit?

f. What is the rms current, I_rms, in amperes, at resonance?

Answer 1

c]! V-IZ. I-= V 5.52 0.33 Ampere. 2 16.67 a] w-21 1910.): 2207. 2- R?+ (x,- XL) r6 XLE LW = 95X10 X 220 TI = 0.066 Xt: 1 : = 1000 - 16:53 w 87.5x18 6xzzon 6005 D] V-12 I= v= 5.52 2 106 Ampebe. 3.46 1 (2-6)*+ (0.065-16:53) 16.67 1 At xuonanej E? X = Xc Lw=1 w. = 10968-16 b] W = 27 (4.58103) WS Inc ab 95% 10 X 87.5 X10 x = 95x100x gtx 10 = 2.69 Xel:1 0.404 aw 87.5x10 xw - Frequency: W = 10963.16 a 1945.64 M₂ ? 1.75 kHz ZT 2T (2-6)²+(2-69-0-404) ² = 3-462 F V=IZ 1- V Z (Now 2= - R) 2012 Ampere I: V5-522 R 2.6