An AC generator with an rms emf of 14.0 V is connected in series with a 0.45-H i

Question

An AC generator with an rms emf of 14.0 V is connected in series with a 0.45-H inductor. The frequency of the source emf Is 75.0 Hz. (a) What is the inductive reactance of the circuit? (b) What is the rms current In the circuit? (c) What are the maximum values of the current and the source emf? (d) Write an expression for the potential difference across the Inductor as a function of time. (Assume V_L (0) - 0. Use the following as necessary: t. Do not use other variables, substitute numeric values. Assume that V_L is in volts and t is in seconds. Do not Include

Explanation / Answer

Vrms = 14 V , L = 0.46 H , f = 75 Hz

(a) inductive reactance XL = wL

XL = 2*3.14*75*0.46 = 216.66 Ohms

(b) Vrms = Irms*XL

14 = I*216.66

Irms = 0.065 A

(c) Imax = 0.065*2^0.5 = 0.092 A

Vmax =Vrms*(2)^0.5

= 14*2^0.5 =19.8 V

(d) VL(0) = 0

V = (19.8)sin(2pi*75t)

V = (19.8V)sin(471.24t)

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