The answers given to me below are wrong please help me A circuit is constructed
ID: 1794059 • Letter: T
Question
The answers given to me below are wrong please help me
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 = 120 V and = 836 radians/second. The values for the remaining circuit components are: R = 70 , L = 84 mH, and C = 11.6F.
A.)
What is Z, the impedance of the circuit?
2)
What is Imax, the magnitude of the maximum value of the current in the circuit?A
3)
What is , the phase angle between the generator voltage and the current in this circuit. The phase is defined to be positive if the generator voltage the current leads, and negative otherwise.
degrees
4)
What is t1, the first time after t = 0 when the voltage across the inductor is zero? seconds
5)
Which of the following statements is true?
The voltage across the generator is zero when the magnitudes of the voltages across the inductor and the capacitor are maximum.
The current in the circuit is zero when the magnitudes of the voltages across the inductor and the capacitor are maximum.
The magnitude of the voltage across the generator is maximum when the magnitudes of the voltages across the inductor and the capacitor are maximum.
The magnitude of the current in the circuit is maximum when the magnitudes of the voltages across the inductor and the capacitor are maximum.
There is no time when the magnitudes of the voltages across the inductor and capacitor are maximum.
6)
What is VC = Vd - Va, the voltage across the capacitor, at time t = 0? Note that VC is a signed number.
V
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Em sin ot) CTEExplanation / Answer
given
V = em*sin(wt)
em = 120 V
w = 836 rad/s
R = 70 ohm
L = 84*10^-3 H
C = 11.6*10^-6 F
a. Z = sqroot(R^2 + (Xl - Xc)^2)
Xl = wL
Xc = 1/w*C
hence
Z = 77.34361 ohm
b. now at time t
from kirchoff's loop law
em*sin(wt) = iR + Ldi/dt + q/C
also, dq/dt = i
hence
q' = i
q" = di/dt
hence
Lq" + Rq' + q/C = em*sin(wt)
84q" + 70,000q' + 86206,896.5517q = 120sin(836t)
hence
for Imax
Imax = Vmax/R = 120/70 = 1.7142 A
c. phi = arctan(Xl - Xc)/R) = -55.8083 deg
d. time period of osscilation for the transient response =T'
T' = 2*pi*/w
w = sqroot(1/LC - R^2/4*L^2)
w = 932 rad/s
T' = 0.0068 s
hence
voltage across inductor is 0 after t = t1 = T/4 = 1.7011 ms
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