Question

An RLC series circuit has a 1.00 kΩ resistor, a 150 mH inductor, and a 25.0 nF capacitor.

a. Find the circuit's impedance (in Ohms) at 500 Hz.

b. Find the circuit's impedance (in ohms) at 7.50 kHz.

c. If the voltage source has Vrms = 408 V, what is Irms (in mA) at each frequency?

mA at 500 Hz = ?

mA at 7.5 Hz = ?

d. What is the resonant frequency (in kHz) of the circuit?

e. What is Irms (in mA) at resonance?

Answer 1

her,

the resistance , R = 1 Kohm = 1000 ohm

inductance , L = 150 mH = 0.15 H

the capacitance , C = 25 nF = 25 * 10^-9 F

a)

at f1 = 500 Hz

the circuit's impedance , Z1 = sqrt(R^2 + (2*pi*f1*L - 1/(2*pi*f1*C))^2)

Z1 = sqrt(1000^2 + (2*pi*500*0.15 - 1/(2*pi*500*25 * 10^-6))^2) ohm

Z1 = 1100 ohm

at f2 = 7.5 KHz = 7500 Hz

the circuit's impedance , Z2 = sqrt(R^2 + (2*pi*f2*L - 1/(2*pi*f2*C))^2)

Z2 = sqrt(1000^2 + (2*pi*7500*0.15 - 1/(2*pi*7500*25 * 10^-6))^2) ohm

Z2 = 7138 ohm

c)

the rms voltage , Vrms = 408 V

the rms current , I1 = Vrms /Z1

I1 = 408 /1100 A = 0.371 A = 371 mA

the rms current of 2 , I2 = Vrms /Z2

I2 = 408 /7138 A = 0.0572 A = 57.2 mA

d)

the resonant frequency , f = 1/2pi * 1/sqrt(L * C)

f = 1/2pi * 1/sqrt(0.15 * 25 * 10^-9)

f = 26003 Hz = 26.003 KHz

e)

the rms current at resonance , Irms = Vrms /R

Irms = 408 /1000 A = 0.408 A

Irms = 408 mA