The voltage of an AC source has been given by the equation v=120sin 628t where v
ID: 1306900 • Letter: T
Question
The voltage of an AC source has been given by the equation v=120sin 628t where v is the instantaneous voltage and t is in seconds. (a) What is the rms value of the voltage? (b) What is the frequency of the AC source? (c) If this voltage is connected in series with a 40 ohm resistor, a 12x10^-6 F capacitor and a 4x10^-3 inductor, find (d) the impedance and (e) the rms current. Assume that the frequency of the source can be varied. (f) Find the resonant frequency of the RLC circuit.
*Please show step by step*
Explanation / Answer
Vmax = 120 volts
a) Vrms = Vmax/sqrt(2) = 120/1.414 = 84.85 volts
b) f = w/(w*pi) = 628/2*pi = 100 hz
c)
d) XC = 1/(2*pi*f*C) = 1/(628*12*10^-6) = 132.7 ohms
XL = 2*pi*f*L = 628*4*10^-3 = 2.512 ohms
z = sqrt(R^2 + (XL-XC)^2)
= sqrt(40^2 + (2.512-132.7)^2)
= 136.2 ohms
e) Irms = Vrms/z
= 84.85/136.2
= 0.63 A
f) f = 1/(2*pi*sqrt(L*C)
= 1/(2*pi*sqrt(4*10^-3*12*10^-6))
= 726.8 Hz
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