Question

The current through a 0.1 Henrys (H) inductor is i(t) = 10 t e^-5tA. Find the voltage across the inductor.

a. v(t) = 10 te^-5t V
b. v(t) = 0.1 (10te^-5t) V
c. v(t) = 5te^-5t V
d. v(t) = (1 - 5t) e^-5t V

Answer 1

Answer: d. $v(t)=(1-5t)e^{-5t}$V

Explanation: Inductance is a property of an inductor: when there is a change in current passing through a conductor, it creates a voltage in the conductor itself and in the other conductors. Inductance unit is Ω.s or henry (H)

So, the relation between Voltage and Current in an inductor is given by

$v=L\frac{di}{dt}$

in which

L is inductance in H

i is current in A

Current is $i(t)=10te^{-5t}$, so, derivative will be:

$\frac{di}{dt}=10e^{-5t}+10t(-5)e^{-5t}$

$\frac{di}{dt}=10e^{-5t}-50te^{-5t}$

$\frac{di}{dt}=10e^{-5t}(1-5t)$

Then, voltage is

$v=0.1.10.e^{-5t}(1-5t)$

$v=(1-5t)e^{-5t}$

Voltage across the 0.1H inductor is $(1-5t)e^{-5t}$ V