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May 12th, 2017, 03:37 AM   #1
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differentiation

Can anybody tell me where I've gone wrong on this question?

An alternating current, i amperes, is given by i = 15 cos (2pi f t)

Calculate the rate of change of current when t = 2 ms and f = 75 Hz.

dy/dx = dy/du × du/dx

y = 15 cos
du/dt = -15sin

= (15) (2pi f) - sin 2 pi f t

= (15) (2 pi × 75) - sin (2pi × 75 × 2×10-3)
= 7067.77 a/s

Last edited by skipjack; May 12th, 2017 at 05:53 AM.
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May 12th, 2017, 03:56 AM   #2
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Quote:
Originally Posted by tommyturner1993 View Post
Can anybody tell me where I've gone wrong on this question?

An alternating current, i amperes, is given by i = 15 cos (2pi f t)

Calculate the rate of change of current when t = 2 ms and f = 75 Hz.

dy/dx = dy/du × du/dx

y = 15 cos
du/dt = -15sin

= (15) (2pi f) - sin 2 pi f t

= (15) (2 pi × 75) - sin (2pi × 75 × 2×10-3)
= 7067.77 a/s
You mean, I think, that u= 2pi ft and y= 15 cos(u). Then dy/du= -15 sin(u) and du/dt= 2pi f. The chain rule gives dy/dt= (2pi f)(-15 sin(2pi ft)= -30pi f sin(2pi ft). You appear to have added the two derivatives rather than multiplying.

Quote:
=(15) (2 pi × 75) - sin (2pi × 75 × 2×10-3)
=7067.77 a/s
With t = 2 ms and f = 75 Hz we have dy/dt= -30pi (75) sin(2pi (75)(2))= (7068 )(sin(942))= (7068 )(-0.459)=-3250.

Last edited by skipjack; May 12th, 2017 at 05:52 AM.
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May 12th, 2017, 04:56 AM   #3
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Assuming frequency is constant since no information is given if or how it changes w/respect to time ...

$i=15\cos(150\pi t)$

$\dfrac{di}{dt} = -2250\pi \sin(150\pi t)$

At $t=0.002 \, sec$ ...

$\dfrac{di}{dt}=-2250\pi \sin\left(\dfrac{3\pi}{10}\right) \approx -5718.6 \, amps/sec$
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May 12th, 2017, 05:10 AM   #4
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Well I redid the question and I have the same answer as you skeeter. Do you know where country boy got the answer -3250 from?

Last edited by skipjack; May 12th, 2017 at 05:54 AM.
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May 12th, 2017, 05:58 AM   #5
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He didn't convert 2 ms to seconds.
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