The output voltage of an AC generator is given by Delta v = (180 V) sin (70 pi t

Question

The output voltage of an AC generator is given by Delta v = (180 V) sin (70 pi t). The generator is connected across a 21.0-Ohm resistor. a. Should the argument for the sine function be in degrees or radians? b. By inspection, what is the maximum voltage? c. By inspection, what is the frequency? d. Find the rms voltage across the resistor. e. Find the rms current in the resistor. f. Find the maximum current in the resistor. g. Find the power delivered to the resistor. h. Find the current when 0.0050 s. i. To make rms current 5A, what inductance must be put in this circuit?

Explanation / Answer

Given Data

V = 180 V * sin (70t)

It is in the form of

V = Vm * sin (2f*t)

Solution :-

(b) By inspection, what is the maximum voltage?

Peak voltage = 180 V

(c) By inspection, what is the frequency?

f = 70/2 = 35 Hz

(d) Find the rms voltage across the resistor.

Vrms= 180/sqrt(2) = 127.3 V

(e) Find the rms current in the resistor.

Irms=Vrms/R= 127.3 / 21.0 = 6.06 A

(f) Find the maximum current in the resistor.

Ip = Vp/R = 180 / 21.0 = 8.57 A

(g) Find the power delivered to the resistor.

Prms= Vrms* Irms

        = 127.3 x 6.06 = 771.44 W

(h) Find the current whent= 0.0050 s.

Evaluate v = (180V)sin(70(pi)(0.0050) / 21 = 7.64 V

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