Simple inductance question: Finding steady state current

[alexdr5398]

Homework Statement

Homework Equations

I = E / R_total

The Attempt at a Solution

I mostly just want to clarify that my thinking is correct. The solution for this problem shows that the current is split evenly between the two paths. Is that because we're assuming that the inductor has no resistance? So since both paths have resistance R, they both draw the same current?

Also, the solution states that the potential different across the inductor goes to zero as dI/dt goes to zero. Why does the current through L not also go to zero? Since:

I_L = E_L / R = 0 / R = 0

 

[gneill]

I mostly just want to clarify that my thinking is correct. The solution for this problem shows that the current is split evenly between the two paths. Is that because we're assuming that the inductor has no resistance?

Yes.

So since both paths have resistance R, they both draw the same current?

Yes. To be more pedantically correct, they both pass or conduct the same current since they share the same potential difference and have the same resistance.

Also, the solution states that the potential different across the inductor goes to zero as dI/dt goes to zero. Why does the current through L not also go to zero? Since:

I_L = E_L / R = 0 / R = 0

As you've stated, the inductor does not have resistance, and certainly not a value of R. Also, E_L is across the inductor only, it doesn't include the series connected resistor that shares its path. that resistance will have its own potential difference due to the current flowing through it.

 

[alexdr5398]

Thank you, that makes sense.

Also, E_L is across the inductor only, it doesn't include the series connected resistor that shares its path.

I don't really understand what inductors are or how they work very well. I just know that they have something to do with changes in current. Is the solution stating that because dI/dt goes to zero, the potential difference across the inductor goes to zero? Or just that both of them go to zero?

 

[gneill]

Thank you, that makes sense.I don't really understand what inductors are or how they work very well. I just know that they have something to do with changes in current. Is the solution stating that because dI/dt goes to zero, the potential difference across the inductor goes to zero? Or just that both of them go to zero?

Inductors react to a change in current by producing an EMF that tries to counter the change. That's what the equation $E = -L~dI/dt$ is saying. The analogy in mechanics is that of a mass that resists a change in velocity thanks to inertia, thus the so-called "inertial force" that makes up the Newton's third law reaction force. The formula there is $F = -M~dV/dt$.

When the current through an inductor is constant so that dI/dt is zero there is no EMF produced. The potential difference across that inductor will be zero for any given constant current. So the two things, zero EMF and zero dI/dt are intimately related. The solution is stating that because dI/dt goes to zero, the potential difference across the inductor goes to zero, as you have written.

 

[alexdr5398]

Inductors react to a change in current by producing an EMF that tries to counter the change. That's what the equation $E = -L~dI/dt$ is saying. The analogy in mechanics is that of a mass that resists a change in velocity thanks to inertia, thus the so-called "inertial force" that makes up the Newton's third law reaction force. The formula there is $F = -M~dV/dt$.

When the current through an inductor is constant so that dI/dt is zero there is no EMF produced. The potential difference across that inductor will be zero for any given constant current. So the two things, zero EMF and zero dI/dt are intimately related. The solution is stating that because dI/dt goes to zero, the potential difference across the inductor goes to zero, as you have written.

Alright, I understand now, thank you!