A circuit is created with an AC generator,a resistor, capacitor and also inductor together shown. The generator voltagevaries over time as ? =Va - Vb =?msin?t, where?m = 120 V and also ? =221 radians/second. The inductance together = 352 mH. The worths for thecapacitance C and also the resistance R room unkown. What is known isthat the current in the circuit leads the voltage throughout thegenerator through ? = 58 degrees and the average power yielded to thecircuit through the generator is Pavg= 68 W.
You are watching: A circuit is constructed with an ac generator, a resistor, capacitor and inductor as shown.
1) What isImax, the amplitudeof the existing oscillations in the circuit?
2) What is R, the valueof the resistance of the circuit?
3) What is C, the valueof the capacitance the the circuit?
4) The worth of ? is now changed,keeping all other circuit parameters constant, until resonance isreached. Just how was ? changed?
"? was decreased" or
"? was increased"
5)What is the mean power ceded to the circuit when it is inresonance?
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current leads voltage
tan (58) = (Xc-Xl)/R
=> Xc -Xl = 1.6*R........... (1)
we understand average power
P = (V_rms)^2 * R / |Z|^2 = 7200* R / R^2 + (Xc-Xl)^2 =7200*R/ R^2+2.56R^2
solving us get
2022.47191/R = 68
R = 29.74223 ohms
Xl= wL = 221*352*10^-3 = 77.792 ohms
now from equation 1 us get
Xc = 1/wc = 1.6R+ Xl = 125.3796
=> C = 1/(221*125.3796) = 36.0895 uF (microfarad)
1) I_max = V/|Z| = 120 / sqrtR^2 + (Xc-Xl)^2 = 120/(1.8868*29.74223) = 2.13836 A
w= 1/sqrt(LC) = 280.5680
w is increased
5) in resonance avg power yielded = 1/2*V^2/R = 242.0800watts
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