Finding Ix in Switch Circuit at Different Times

[jeuceda]

Homework Statement

Assume that the switch in the figure has been closed for a long time and opens after in t=0.
Find Ix in a) 0- b)0+ c) 40ms

The Attempt at a Solution

Switch is opened in t=0, current flows only in the 10Ω resistor, Ix=3v/10Ω= 0.3A-> 0-
0+ --> 3v/10=0.3A
Not sure if both currents are the same, and for the 40ms, when solving the equation (τ=L/R) τ (tau) results in a small number.

 

[axmls]

Do you think it's possible for the current through an inductor to change instantaneously?

It might help to see your work for part c in order to check it.

 

[jeuceda]

Do you think it's possible for the current through an inductor to change instantaneously?

It might help to see your work for part c in order to check it.

No couldt change instantaneously.
this is what i have for part c
τ=L/R -> (500mH)/70Ω=7.14ms

i(t)= i(∞)-(i(∞)-i(0+))e^(-t/τ)
i(40)= ?

That where I am stuck

 

[NascentOxygen]

Hi jeuceda.

The Attempt at a Solution

when the switch is open Ix=3v/10Ω= 0.3A

What assumptions allow you to say this?

When the switch is closed Ix=0.3A

How did you calculate this?

Not sure if both currents are the same, and for the 40ms, when solving the equation τ (tau) results in a small number.

You mention an equation. What is your equation, exactly?

It is clearer when you include a phrase such as "at the moment before the switch is closed ...", or "once the switch has been open for a long time ...", to confirm precisely what you are talking about.

BTW, the diagram is ambiguous; it is not clear from the diagram whether at time t=0 the switch is opened after having already been closed for a long time, or whether it is being closed at t=0 having prior to this been open for a long time. The textbook's double-headed arrow would be better drawn with only one arrow head.