An AC voltage of the form ?v = 80 sin 340t where ?v is in volts and t is in seco

Question

An AC voltage of the form ?v = 80 sin 340t where ?v is in volts and t is in seconds, is applied to a series RLC circuit. If R = 30.0 ?, C = 30.0 µF, and L = 0.220 H, find the following.

(a) the impedance of the circuit ?

(b) the rms current in the circuit A

(c) the average power delivered to the circuit W

An AC voltage of the form Av 80 sin 340t where Av is in volts and t is in seconds, is applied to a series RLC circuit. If R = 30.0 , C = 30.0 F, and L = 0.220 H, find the following (a) the impedance of the circuit (b) the rms current in the circuit (c) the average power delivered to the circuit

Explanation / Answer

a) Now = 340

so Z = sqrt(R^2 + (L - 1/C)^2) = sqrt(30^2 + (340*.22 - 1/340*30x10^-6)^2) = sqrt(1438.24) =37.93

impedence Z=37.93 or 38 (Ans of part a)

b) I rms = Vmax*sqrt(2)/2/Z = 80*sqrt(2)/2/38 = 1.4886A or 1.49 A

Therefore,rms current=1.49A(Ans)

c) P = vrms*irms*cos() where = arctan((L - 1/C)/R) = arctan((340*.220 - 1/340*30x10^-6)/30) = -37.59o or -37.6 degrees.

So P = 80/sqrt(2)*1.49*cos(-37.6) = 66.97W or 67W.(Ans)

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