Question

The output voltage of an AC generator is given by ?v = 121 V sin (32?t). The generator is connected across a 0.007 H inductor. Find the following.

(a) frequency of the generator?=____ Hz

(b) rms voltage across the inductor?=____ V

(c) inductive reactance?=____ ohms

(d) rms current in the inductor?=____ A

(e) maximum current in the inductor?=____ A

(f) average power delivered to the inductor?=____ W

(g) Find an expression for the instantaneous current. (Use the following as necessary: t.)

" i=_________ "

(h) At what time after t = 0 does the instantaneous current first reach 1.00 A? (Use the inverse sine function.)?=_____ s

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Answer 1

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The output voltage of an AC generator is given by ?v= 580 V sin (120?t). The generator isconnected across a 1.200 H inductor. Findthe following.

(a) frequency of the generator
1 Hz

(b) rms voltage across the inductor
2 V

(c) inductive reactance
3?

(d) rms current in the inductor
4 A

(e) maximum current in the inductor
5 A

(f) average power delivered to the inductor
6 W

(g) Find an expression for the instantaneous current. (Use thefollowing variables as necessary: t, pi.)
7

(h) At what time after t = 0 does the instantaneouscurrent first reach 1.00 A? (Use the inverse sine function.)
8 s

     

answer

Inductance L = 1.2 H
Given  ?V = 580 V sin (120?  t)

Compare this with   ?V = Vo sin ( 2f ?t ) we get

(a). Frequency of the generator   f = 120 / 2 = 60Hz

(b). Rms voltage V = Vo/ ?2

                              =580 / ?2 = 410.12 Volt

(c). Inductive reactance X = L( 2?f )

                                        = 452.38 ohm

(d). rms current I= V / X

                          = 0.9065 A

(e). maximum current I o = ?2 * I = 1.282 A

(f). Average power P = IV

                                  =371.77 W

(g). Instantaneous current I ' = ?V / X

                                           = 1.282 sin ( 120?t )

(h ) current I ' = 1A

plug it in above we get   1 = 1.282 sin (120?t)

                    120 ?t = 1/ 1.282 = 0.7799

                             t = 0.00206 s