Engineering Inductor Voltage Maximum and Maximum Voltage Calculation

AI Thread Summary
The discussion focuses on calculating the maximum voltage across a 25mH inductor given a specific current function. The user attempts to find the time at which the voltage is maximum by taking the derivative of the current equation and setting it to zero. Initial calculations lead to confusion regarding the correct value of time, with the user mistakenly using an angle instead of the time variable. After correcting the variable substitution, the correct time for maximum voltage is found to be approximately 0.00277 seconds. The conversation highlights the importance of careful variable management in calculus-based problems.
Zarathuztra
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Homework Statement


The current in a 25mH inductor is known to be - 10A for t <= 0 and (-10cos400t - 5sin400t)e^-200t A for t >= 0. Assume the passive sign convention.

Part A: At what instant of time is the voltage across the inductor maximum?
Part B: What is the maximum voltage?

Homework Equations


V=L*di/dt


The Attempt at a Solution



I took the derivative of (-10cos400t - 5sin400t)e^-200t, then took the derivative again, set to zero, and found the value of t at that point.

5000*e^(-200t)*sin(400t)

1000000*e^(-200t)(2cos400t - sin400t) = 0 @ t = 0.01339 s

Where am I going wrong? Am I missing something?
 
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t = 0.01339 s doesn't look like a zero of that function to me...
 
your right, that's way off... looking at it again.

I need 2cos400t - sin400t to equal 0...

2cosx = sinx
2 = tanx
arctan(2) = x

x = 1.107s

this didn't work.. is my derivative correct? I'm pretty sure my algebra and trig were correct.
 
Last edited:
Zarathuztra said:
your right, that's way off... looking at it again.

I need 2cos400t - sin400t to equal 0...

2cosx = sinx
2 = tanx
arctan(2) = x

x = 1.107s

this didn't work.. is my derivative correct? I'm pretty sure my algebra and trig were correct.

You've solved for the angle, x. But the angle is not t...
 
hahaha, what a silly mistake, I used a variable in place of 400t and didn't sub the variable out... x/400 = t so, 1.107/400 = t = .0027679s
 
Yes, that looks much better :smile:
 

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