Max Current Time for Inductance Q1: Solve for t

[shifty101uk]

1. i = 10te^(-5t), at what instant of time is the current maximum?

first I differentiated i, using the product rule.

di/dt = (10e^(-5t)) (1-5) , that's what I got after simplifying, I am pretty certain this is correct. My confusion comes in when taking natural logarithms.

if ln(e(^1)) = 1 then ln(e(^-5t)) = -5t, I am just not entirely sure what to do from here but I gave it a shot.

10ln 5t(1-5) = 0

ln (50t-250t) = 0**

ln (50/250) = t.

The answer in the book is di/dt = 0 when t=1/5.

If anyone can clear any of that up for me Id be very grateful.

I have just spotted a glaring error** the 10 should be taken as a power, not a product.

so it should be ln((5t/25t)^10) = 0

how do I calculate t?

 

[AlephZero]

Your differentiation di/dt = (10e^(-5t)) (1-5) is wrong.

It should be di/dt = (10e^(-5t)) (1-5t)

Fixing that mistake makes the question a lot easier!

 

[shifty101uk]

ahhhh thankyou, I really should double check more often. I was nearly pulling my hair out over that!