A series RLC circuit has a 242 Hz resonant frequency, and is driven by an AC voltage source at 315 Hz. The circuit has a 75.0 resistor and a 66.0 mH inductor. The maximum current is 1.20 A.
a) Find the capacitance in the circuit.
b) Find the maximum voltage of the source.
c) Find the average power of the circuit
d) Find the phase angle .
a)
resonant frequency, fo = 242 Hz
AC frequency, f = 315 Hz
resistance, R = 75 ohm
inductance, L = 66 mH
max current , Io = 1.2 A
a)
We know , resonant frequency, fo = 1/sqrt(LC)
So, C = 1/(fo^2*L) = 1/(242^2*66*10^-3)
= 2.59*10^-4 F = 259 uF <-----------answer
b )
maximum voltage = maximum current*R = Io*R = 1.2*75 = 90 V
c)
Z = sqrt(R2+(2*pi*f*L-1/(2*pi*f*C))^2) = sqrt(75^2+(1*3.14*315*0.066-1/(2*3.14*315*2.59*10^-4))^2)
= 98.2 ohm
So, power factor = cos = R/Z = 75/98.2 = 0.764
Imax = 1.2 A
Vmax = 90 V
average power, Pavg = Imax*Vmax*cos / 2 = 1.2*90*0.764/2 = 41.3 W <-------answer
d)
phase angle = acos(0.764) = 40.2 degrees <-------------answer
A series RLC circuit has a 242 Hz resonant frequency, and is driven by an AC...
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