The output voltage of an AC generator is given by ?v = (200 V) sin (70?t). The g

Question

The output voltage of an AC generator is given by ?v = (200 V) sin (70?t). The generator is connected across a 19.0-? resistor.
(a) By inspection, what is the maximum voltage?
=__________ V

(b) By inspection, what is the frequency?
=__________Hz

(c) Find the rms voltage across the resistor.
=__________V

(d) Find the rms current in the resistor.
=___________A

(e) Find the maximum current in the resistor.
=__________A

(f) Find the power delivered to the resistor.
=___________W

(g) Find the current when t = 0.0050 s.
=___________A

(h) Should the argument of the sine function be in degrees or radians? Which one of the following:

The argument of the sine function should be in degrees. OR
The argument of the sine function should be in radians.

Explanation / Answer

(a) maximum voltage= 200 V [ when sin(70t) =1]

(b) frequency= / 2.

here, = coefficient of t= 70

=> f=70/2= 35 Hz

(c)rms voltage= peak voltage/2= 200/2=141.42 V

(d)rms currect= rms voltage/ resistance= 141.42/19=7.44 A

(e)peak current= peak voltage/ resistance= 200/19=10.52 A

(f)Power delivered to the resistor=(1/2)* rms voltage* rms current=0.5*141.42* 7.44=526.08 W

(g)current= voltage/ resistance=200 sin (70t)/19=

at t=0.005 s, current=200 sin (70*0.005)/19=0.2 A

(h) the angle should be in radian. This is because to keep the dimensions same, the parameters of the sine function must be dimensionless.

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