# Parallel Magnetic Circuit

**Definition:** A magnetic circuit having two or more than two paths for the magnetic flux is called a **parallel magnetic circuit**. Its behavior can be compared to the parallel electric circuit.The parallel magnetic circuit contains different dimensional areas and materials having various numbers of paths.

The above figure shows parallel magnetic circuit. In this circuit, a current carrying coil is wound on the central limb AB. This coil sets up the magnetic flux φ_{1} in the central limb of the circuit. The flux φ_{1} which is in the upward direction is further divided into two paths namely ADCB and AFEB. The path ADCB carries flux φ_{2}, and the path AFEB carries flux φ_{3}. It is clearly seen fro the above circuit that

φ_{1 }= φ_{2} + φ_{3}

The two magnetic paths ADCB and AFEB forms the parallel magnetic circuit, thus, the ampere turns (ATs) required for this parallel circuit are equal to the ampere turns (ATs) required for any one of the paths.

As we know, reluctance is

If S_{1} = reluctance of path BA will be

S_{2 }=reluctance of path ADCB will be

S_{3} = reluctance of the path AFEB will be

Therefore, the total MMF or the total Ampere turns required in the parallel magnetic circuit will be the sum of all the individual parallel paths.

Total mmf required = mmf required for the path BA +mmf required for the path ADCB + mmf required for the path AFEB

Where φ_{1}. Φ_{2}, φ_{3} are the flux and S_{1,} S_{2}, S_{3} are the reluctances of the parallel path BA, ADCB and AFEB respectively.