AC Circuit in Resonance 1 2 3 4 5 6 7 A circuit is constructed with an AC genera
ID: 1608492 • Letter: A
Question
AC Circuit in Resonance
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A circuit is constructed with an AC generator, a resistor, capacitor and inductor as shown. The generator voltage varies in time as = Va - Vb = msint, where m = 24 V and = 161 radians/second. At this frequency,the circuit is in resonance with the maximum value of the current Imax = 0.74 A. The capacitance C = 126F. The values for the resistance R and the inductance L are unknown.
1)
What is L, the value of the inductance of the circuit?
mH
2)
What is Umax,C, the value of the maximum energy stored in the capacitor during one cycle?
J
3)
What is U, the total energy dissipated in the circuit in one cycle?
J
4)
What is Q, the quality factor of this ciruit?
5)
What is R, the value of the resistance of the circuit?
E," sin(wt) n Sin(a) t a C L C R b 110000 dExplanation / Answer
max = 24 V, Imax = 0.74 A, C =126 uF, w =161 rad/s
(1) at resonance
wo = (1/LC)^0.5
161 = (1/(L*126*10^-6))^0.5
L = 306 mH
(2) Umax =0.5CV^2
Umax = 0.5*126*10^-6*24*24
Umax = 0.0363 J
(3) T = 2pi/w = 2*3*14/161 =0.522 s
P = IV
U = P*T = 0.74*24*0.522
U = 9.27 J
(4) emax = Imax*R
24 = 0.74*R
R = 32.4 ohms
Q = wo*L/R
Q = 161*0.306/32.4
Q = 1.52
(5) R = 32.4 ohms
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