Find the resultant in the form v = R sin ( 4t + α )

Question

The values are:

 

V₁ = 6.928 sin 4t

 

V₂ = 4.0 cos 4t

 

 

 

1. Find the resultant in the form

v = R sin ( 4t + )

 

1. Find the first time that the resultant voltage rises to 7.2 volts

Answer 1

a)

Convert the voltages to rectangular coordinates.

V₁ = 6.928 sin (4t+0)

V₁ = 6.928 cos(0°)i +6.928 sin(0°)j

   = 6.928i

V₂ = 4 sin (4t+0)

V₂ =4 cos(0°)i +6.928 sin(0°)j

    =4i

Add two voltages

V₁ + V_{2 =}6.928i  +  4i = 10.928 i

Resultant is 10.928 V

 Phase= arc tan (j -component/i-component) =arc tan (0/10.928) =0

V = 10.928(4t)

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b)

Find the first time t

V₁ = 10.928 sin 4t

18.128 =10.928 sin 4t

 sin 4t =0.659

4t =41.213° = 0.7189 rad

t =0.179 s