An ac generator produces emf according to E(t) = Vm sin(dt - /4). The current in

Question

An ac generator produces emf according to E(t) = Vm sin(dt - /4). The current in the circuit attached to the generator is given by i(t) = Im sin(dt + /4). (a) At what time after t = 0 does the generator emf first reach a maximum? (b) At what time after t = 0 does the current first reach a maximum? (c) The circuit contains a single element other than the generator. Is it a capacitor - type "0", an inductor - type "1", or a resistor - type "2"? (d) What is the value of the capacitance, inductance, or resistance, as the case may be? Express your answers in terms of Vm, Im, d, and .

Explanation / Answer

given

E(t) = Vm sin(dt - /4)

i(t) = Im sin(dt + /4)

a )

At what time after t = 0 does the generator emf first reach a maximum

E(t) = Vm

where

sin(dt - /4) = 1

(dt - /4) = sin-1 ( 1 )

(dt - /4) = /2

dt = 3/4

d = 3/4t

b )

i(t) = Im

where

sin(dt + /4) = 1

(dt + /4) = sin-1 ( 1 )

(dt + /4) = /2

dt = /2 - /4

c )

current reaches to maximum

this is the reason why

The circuit contains a single element other than the generator is an inductor - type "1"

d )

the value of the inductance is

VL = IL XL  

XL = d L

VL = IL d L  

then

L = VL / IL d   

or

L = Vm / IL d

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