Inductor Voltage Maximum and Maximum Voltage Calculation

[Zarathuztra]

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?

 

[gneill]

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

 

[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.

 

[gneill]

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...

 

[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

 

[gneill]

Yes, that looks much better