Flux Linkage through two coils

[123yt]

1. Coil 1 has an inductance of 4.50×10-2 H and 140 turns. Coil 2 has an inductance of 8.00×10^-2 H and 230 turns. The coils are rigidly positioned with respect to each other, their mutual inductance is 5.00×10^-3 H. A 7.00×10^-3 A current in coil 1 is changing at a rate of 7.0 A/s.

What flux links coil 2?
2. M = N2 * Flux Linkage / i1
3. Mutual inductance = 5*10^-3
Current in first wire = 7 * 10^-3
Turns in second wire = 230

Flux linkage through second wire = 5 * 10^-3 * 7 * 10^-3 / 230 = 1.52*10^-7 Wb
Solution doesn't work.

 

[anathema]

Hello,

Thank you for sharing this problem with the forum. I would like to provide a more detailed explanation and solution to this problem.

First of all, let's define some terms and equations that are relevant to this problem.

- Inductance (L): a property of a coil that describes its ability to store energy in the form of a magnetic field when a current flows through it. It is measured in Henrys (H).

- Mutual inductance (M): a property of two coils that describes how a changing current in one coil induces a voltage in the other coil. It is measured in Henrys (H).

- Flux linkage (Φ): the amount of magnetic flux that passes through a coil. It is measured in Weber (Wb).

- Current (I): the flow of electric charge through a conductor. It is measured in Amperes (A).

Now, let's look at the given information in the problem:

- Coil 1 has an inductance of 4.50×10^-2 H and 140 turns.
- Coil 2 has an inductance of 8.00×10^-2 H and 230 turns.
- Mutual inductance between the coils is 5.00×10^-3 H.
- Current in coil 1 is changing at a rate of 7.0 A/s.

Using the equation for mutual inductance, we can calculate the flux linkage through coil 2:

M = N2 * Φ / I1

Where:
- N2 is the number of turns in coil 2
- Φ is the flux linkage through coil 2
- I1 is the current in coil 1

Substituting the given values, we get:

5.00×10^-3 H = 230 * Φ / 7.0 A/s

Solving for Φ, we get:

Φ = 1.52×10^-6 Wb

Therefore, the flux linkage through coil 2 is 1.52×10^-6 Wb.

I hope this explanation helps to clarify the solution to this problem. Please let me know if you have any further questions or concerns.