An ac generator emf has emf = m sin (?d t - ?/4), where m = 25.0 V and ?d = 420

Question

An ac generator emf has emf = m sin (?d t - ?/4), where m = 25.0 V and ?d = 420 rad/s. The current produced in a connected circuit is i(t) = I sin(?d t - 3?/4), where I = 630 mA. (a) At what time after t = 0 does the generator emf first reach a positive maximum? ---------------s (b) At what time after t = 0 does the current first reach a positive maximum? ------------------s c) The circuit contains a single element other than the generator. Is it a capacitor, an inductor, or a resistor? True___(inductor) Justify your answer.

Explanation / Answer

a)The generator emf is a maximum when sin(dt –/4) = 1

dt-/4 =(/2)±2n

The first time this occurs after t = 0 is when

dt-/4=/2 i.e when n=0

t=3/4d

t=3/4*420 =5.61*10-3s or 5.61ms

b)

The current is a maximum when sin(dt-3/4)=1

dt-3/4 =(/2)±2n

The first time this occurs after t = 0 is when

dt-3/4 =/2 i.e when n=0

t=5/4d =5/4*420 =9.35*10-3s or 9.35ms

c)The current lags the emf by (+/2) rad, so the circuit element must be an inductor.

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