Please answer all parts please. An ac generator has emf epsilon = epsilon_m sin(

Question

Please answer all parts please.

An ac generator has emf epsilon = epsilon_m sin(omega_dt - pi/4), where epsilon_m = 40.0 V and omega_d = 447 rad/s. The current produced in a connected circuit is i(t) = I sin(omega_d t - 3 pi/4), where I = 769 mA. At what time after t = 0 does (a) the generator emf first reach a maximum and (b) the current first reach a maximum? (c) The circuit contains a single element other than the generator. Is it a capacitor, an inductor, or a resistor? (d) What is the value of the capacitance, inductance, or resistance, as the case may be? (a) Number Units (b) Number Units (c) (d) Number Units

Explanation / Answer

the emf = max sin(dt - /4)   ................. (1)

   here , emf max = 40 V

            angular speed d = 447 rad/s

current i(t) =I sin(dt - 3/4)   ..................... (2)

here , current I = 620 mA = 620*10-3 A

a)

the emf is maximum at = 900 = /2   (since sin90 = 1)

so , (dt - /4) = /2

         dt = /4+ /2

         dt = 3/4

time t = 3/4d

         = 3(3.14)/4(447 rad/s)

       = 5.26*10-3 s

b)

the current is maximum at = 900 = /2

so , (dt - 3/4) = /2

       dt = 3/4 + /2

   time t = 5/4d

             = (5)(3.14) / (4)(447 rad/s)

             = 8.78*10-3 s

c)

here , the the voltage is leading the current .

so , the single element is inductor.

d)

the inductive reactance is

                 XL = /I   ................ (3)

and XL = dL    ................. (4)

compare eq (3) and (4) , we get

     / I = dL

therefore , inductance L = / I d

                                     = (40 V) / (769*10-3 A)( 447 rad/s)

                                     = 116.36 mH

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