The plate on the back of a personal computer says that the machine draws 3.1 A from a 120 V, 60 Hz line. For this PC, what are (a) the average current, (b) the average of the square of the current, and (c) the current amplitude.

Respuesta :

Answer:

a) 0 A

b)9.6 A

c)4.38 A

Explanation:

Given that

[tex]I_{r.m.s}=3.1\ A[/tex]

[tex]V_{r.m.s}=60\ V[/tex]

We know that

[tex]I_{r.m.s}=\sqrt{\int_{0}^{T}\dfrac{1}{T}I^2(t)\ dt}[/tex]

Lets take current in sinusoidal  from ,so the average values of sinusoidal function will be zero.

So the average current = 0 A

[tex]{\int_{0}^{T}\dfrac{1}{T}I^2(t)\ dt}\ is\ the\ average\ of\ the\ square\ of\ the\ current.[/tex]

Average of the square of the current

[tex]Average\ of\ the\ square\ of\ the\ current\ = I_{r.m.s}^2 [/tex]

 Average of the square of the current = 9.6 A

The amplitude of current

[tex]I_o=\sqrt 2\ I_{r.m.s}[/tex]

So now by putting the values

[tex]I_o=\sqrt 2\ \times 3.1\ A[/tex]

[tex]I_o=4.38\ A[/tex]