For a coil having a magnetic circuit of constant reluctance, the flux is directly proportional to the current. ... Hence as the flux increases, the current also increases.

Flux in a Coil and its Relationship with Current

The flux in a coil refers to the total magnetic field passing through the coil. It is a measure of the total magnetic lines of force that are linked with the coil. The flux is directly related to the current flowing through the coil. Let's explore this relationship in detail:

1. Magnetic Circuit with Constant Reluctance:
- A magnetic circuit consists of a closed loop path through which magnetic flux can flow. It includes magnetic materials such as iron cores, air gaps, and coils.
- The reluctance of a magnetic circuit is similar to the resistance in an electrical circuit. It represents the opposition to magnetic flux flow.
- In this question, it is stated that the magnetic circuit has a constant reluctance. This means that the magnetic circuit does not change its reluctance value with respect to the current flowing through it.

2. Relationship between Flux and Current in a Coil:
- According to Ampere's law, the magnetic field created by a current-carrying conductor is directly proportional to the current flowing through it.
- In a coil, the magnetic field produced by the current flowing through the wire creates a magnetic flux that is linked with the coil.
- The flux linkage is directly proportional to the current flowing through the coil. As the current increases, the magnetic field strength increases, resulting in a higher flux linked with the coil.
- Therefore, the flux in a coil is directly proportional to the current flowing through it.

3. Implications of the Relationship:
- The relationship between flux and current is important in various applications of coils, such as electromagnetic induction, transformers, and inductors.
- For example, in a transformer, the primary coil creates a varying magnetic field due to the alternating current flowing through it. This changing magnetic field induces a voltage in the secondary coil through mutual induction. The amount of voltage induced depends on the flux linkage, which is directly proportional to the current in the primary coil.
- Similarly, in an inductor, the magnetic field generated by the current flowing through the coil stores energy. The amount of energy stored is directly related to the flux linkage, which is again proportional to the current.

Conclusion:
In conclusion, the flux in a coil with a magnetic circuit of constant reluctance is directly proportional to the current flowing through it. This relationship is fundamental in understanding the behavior of coils in various electrical and electronic applications.