A voltage source, Vs= 180sin760t is in series with an inductor L = 435 mH, a cap

Question

A voltage source, Vs= 180sin760t is in series with an inductor L = 435 mH, a capacitor C = 2 microFarads, and a                     resistor R = 240 ohms .

a)  What is the phase angle of this circuit?  Does the current l lead the total voltage or lag behind it?

b) What is the average power delivered by the battery and dissipated by each component?

c) What is the instantaneous current in the circuit, I, Vs, V(r),V(L),V(C) at t = 3 seconds?

d) When is the first time after t= 3 seconds when the voltage of the inductor is three times larger than the voltage of the resistor and what are their values at that time?

e) Answer a-c at the resonance frequency

Explanation / Answer

Imax = Vmax/impedence = 0.4435A

a)      Phase angle = tan_inverse(reactance/R) = 0.938 Rad = 53.75 degree

As Xc > XL so, current l lead the total voltage.

b)     average power delivered by the battery = Vrms*Irms*cos(phase) = 23.61W

power dissipitated by R = Irms^2*R = 23.61W

power dissipitated by L =0

power dissipitated by C =0

c)       I(t) = Imax sin(760t + 0.938) = 0.0626 A

Vs = 180sin760t = -128.655 V

Vr = 0.0626 A * 240 = 15.024V

Vc = 0.0626*657.895 = 41.184V

VL = 0.0626*330.6 = 20.6955 V

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