# Homework Help: Inductor First order circuits

1. Oct 10, 2012

### Zarathuztra

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
V=L*di/dt

3. 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?

2. Oct 10, 2012

### Staff: Mentor

t = 0.01339 s doesn't look like a zero of that function to me...

3. Oct 10, 2012

### Zarathuztra

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: Oct 10, 2012
4. Oct 10, 2012

### Staff: Mentor

You've solved for the angle, x. But the angle is not t...

5. Oct 10, 2012

### Zarathuztra

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

6. Oct 10, 2012

### Staff: Mentor

Yes, that looks much better

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