What happens to a coil of wire as current is increased?

[alexdr5398]

Homework Statement

Homework Equations

L = (N * F_b) / I (where F_b is the magnetic flux)
emf = -L * (dI/dt)

The Attempt at a Solution

I originally thought that the inductance would decrease since it is inversely proportional to current. But, looking at the equation for emf, that would also mean that emf would decrease since L is decreasing and dI/dt is constant.

 

[berkeman]

Homework Statement

View attachment 194727

Homework Equations

L = (N * F_b) / I (where F_b is the magnetic flux)
emf = -L * (dI/dt)

The Attempt at a Solution

I originally thought that the inductance would decrease since it is inversely proportional to current. But, looking at the equation for emf, that would also mean that emf would decrease since L is decreasing and dI/dt is constant.

Your answer looks correct to me. The EMF is constant since the increase in I is linear. The inductance is a physical quantity, not affected by current (for an air core inductor). If the inductor had a ferrite or iron core, would that change your answer?

 

[TSny]

L = (N * F_b) / I (where F_b is the magnetic flux)

I originally thought that the inductance would decrease since it is inversely proportional to current.

If the current increases, would anything else on the right side of the above equation change?

 

[alexdr5398]

Your answer looks correct to me. The EMF is constant since the increase in I is linear. The inductance is a physical quantity, not affected by current (for an air core inductor). If the inductor had a ferrite or iron core, would that change your answer?

If the current increases, would anything else on the right side of the above equation change?

Oh, so the flux is increased by the increase in current which counters the current in the denominator?

And since inductance is a physical quantity, it can never be changed by the properties in a circuit?

 

[TSny]

Oh, so the flux is increased by the increase in current which counters the current in the denominator?

Yes. If the current doubles, then the flux doubles. So, the formula would leave L unchanged.

And since inductance is a physical quantity, it can never be changed by the properties in a circuit?

Yes. The inductance is determined by the physical properties of the inductor (size, shape, number of wraps, type of core, etc.) as berkeman pointed out.