Question

The current from an AC source is given by:
I(t) = 10.10 sin(70.0 t + 0.830 ) mA,
where t is given in seconds.
(a) What is the RMS current I_RMS?
mA
(b) What is the frequency f?
Hz
(c) If the phase shift were given in degrees, what would its value be?
degrees
(d) What is the time t₀ closest to t = 0 when the current vanishes?
ms

Answer 1

Note that

Irms = Imax / sqrt(2)

Here, Imax = 10.10 mA, thus,

Irms = 7.142 mA   [ANSWER, PART A]

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If

I = Io sin(wt + p)

f = w/[2 pi]

Thus,

f = 70.0 /s / [2 pi]

= 11.14 Hz [ANSWER, PART B]

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The phase shift here is p, in,

I = Io sin(wt + p)

Here,

p = 0.830 rad

In degrees,

p = 47.6 degrees [ANSWER, PART C]

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The current vanishes when the quantity inside sin is 0 or pi.

If it is 0:

70.0t + 0.830 = 0 ---> t = -0.0119 s
70.0t + 0.830 = pi --> t = 0.0330 s

Thus, as -0.0119 is closer, then the closest time to t = 0 is,

t = -0.0119 s = -11.9 ms   [ANSWER, PART D]