An RLC circuit of an AC voltage source is connected in series to a resistor, a c

Question

An RLC circuit of an AC voltage source is connected in series to a resistor, a capacitor, and an inductor. At the resonant frequency, the inductive reactance is 68 Ohms. What is the inductive reactance at a frequency which is at a frequency a factor of 4.7 times less than the resonant frequency? An RLC circuit of an AC voltage source is connected in series to a resistor, a capacitor, and an inductor. At the resonant frequency, the inductive reactance is 8.7 Ohms. What is the capacitive reactance at a frequency which is at a frequency a factor of 3.0 times less than the resonant frequency? An RLC circuit of an AC voltage source with a maximum voltage of 32.3 wits is connected in series to a resistor, a capacitor, and an inductor. At the resonant frequency, the RMS current is 5.9 amps. What is the average power at the resonant frequency in Watts?

Explanation / Answer

Given an RLC series circuit

Question 8

   with inductive reactance at resonance is XL1 = 68 ohm

we know that the inductive reactance is XL1 = W*L = 2pi*f*L

and the inductive frequency (XL2) at which the frequency of the is 4.7 times less thant the frequency at resonance that is

           f2 = (1/4.7)f1

   XL1/XL2 = f1/f2

   XL2 = XL1*f2/f1
   = 68(f1/4.7)/f1

   = 68/4.7 ohm

   = 14.47 ohm

Question 9

   inductive reactance at resonance is XL1 = 8.7 ohm
at resonance the inductive reactance = capacitive reactance so Xc = 8.7 ohm

we know that the inductive reactance is XC1 = 1/W*C = 1/(2pi*f*C)

and the capactive reactance (XC2) at which the frequency of the is 3 times less thant the frequency at resonance that is

           f2 = (1/3)f1

   XC1/XC2 = f2/f1

   XC2 = XC1*f1/f2
   = 8.7*f1/(1/3)f1
   = 8.7*3
   = 26.1 ohm

   = 68/4.7 ohm

   = 26.1 ohm

Question 10

  
   maximum voltage is Vmax = 32.3 V
   rms current is i rms = 5.9 A

   the maximum current is Imax = sqrt(2) (irms) = sqrt(2) (5.9)

now power P max = Vmax*Imax = 32.3*sqrt(2) (5.9) W = 269.5067 ohm

now the average power is P avg = Pmax/2 = 269.5067 /2 = 134.75335 W

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