Five infinite-impedance voltmeters, calibrated to read RMS values, are connected
ID: 2123819 • Letter: F
Question
Five infinite-impedance voltmeters, calibrated to read RMS values, are connected as shown. NOTE: for sinusoidal currents and voltages, RMS values are equal to maximum values (amplitudes) divided by the square root of two. The given values are
(c) For this case in which the AC generator is operating at the resonance angular frequency, consider the actual instant of time at which the EMF of the generator is +16.500 V and increasing. At this particular instant of time, what are the actual voltages across the passive circuit elements, or combinations of those elements? HINT: recall that the sum of the voltages of the passive elements must equal the generator EMF at every instant of time.
voltage across the resistor:
voltage across the inductor:
voltage across the capacitor
Five infinite-impedance voltmeters, calibrated to read RMS values, are connected as shown. NOTE: for sinusoidal currents and voltages, RMS values are equal to maximum values (amplitudes) divided by the square root of two. The given values are R = 220.0 ohms, L = 0.430 H , and C = 5.60 %u03BCF. The amplitude of the generator EMF is 33.0 V. For this case in which the AC generator is operating at the resonance angular frequency, consider the actual instant of time at which the EMF of the generator is +16.500 V and increasing. At this particular instant of time, what are the actual voltages across the passive circuit elements, or combinations of those elements? HINT: recall that the sum of the voltages of the passive elements must equal the generator EMF at every instant of time.Explanation / Answer
c)
for resonance,
w= 1/(sqrt(LC)) = 1/(sqrt(0.43*5.6*10^-6)) = 644.42 radians/s
16.5 = 33 sin(wt)
so, wt = sin-1(16.5/33) = 30 degrees = 0.523 radians
t = 0.523/644.42 = 0.811*10^-3 seconds = 0.811 ms
voltage across resistor = V = 16.5 V
current in resistor = 16.5/220 = 0.075 A
voltage across inductor = j*w*L*i = j*644.42*0.43*0.075 = 20.78 j V = 20.78 V in magnitude
voltage across capacitor = -20.78 j V = 20.78 V in magnitude.
Because in resonance, voltage of capacitor will be equal and opposite to that of inductor.
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