Question

There is $900mA$ of current through a wire with $40$ turns. What is the reluctance of the circuit if the flux is $400\mu Wb$?

& A.14,00At/Wb \\\ & B.1,440At/Wb \\\ & C.9,000At/Wb \\\ & D.90,000At/Wb \\\ \end{aligned}$$

Answer 1

Magnetic reluctance is the opposition to the change in magnetic flux. We know that the change in magnetic flux can induce current, and an alternating current can produce a magnetic field. The opposition to this phenomenon is called the magnetic reluctance.

Formula used:
$R=\dfrac{ni}{\phi}$

Complete step-by-step answer:
Magnetic flux is the number of magnetic field lines passing through a given area. If the number of magnetic field lines passing through a given area is more, then the magnetic flux through that area is said to be high. This magnetic flux plays an important role in the electromagnetic induction of electric current. The flux is generally measured using the flux meter. The SI unit of magnetic flux is weber or Wb which is volt-second. The CGS unit of magnetic flux is maxwell, named after the scientist James Clerk Maxwell, who gave the electromagnetic theory.
Also, one weber is the magnetic flux produced due to flow of one volt of emf for one sec in a circuit.
Here, we have the current in the circuit as $i=900mA=900\times 10^{-3}=0.9A$
We also have the number of turns in the wire as$n=40$ and the flux in the circuit as $\phi=400\mu Wb=400\times10^{-6}=4\times 10^{-4}Wb$
Then the magnetic reluctance is given by $R=\dfrac{ni}{ \phi}$
Then, substituting the values we get, $R=\dfrac{40\times 0.9}{4\times 10^{-4}}=90000At/Wb$
Hence the answer is $D.90,000At/Wb$

So, the correct answer is “Option D”.

Note: This is often observed in transformers, where the current in the turnings is produced due to the change in the magnetic field. However, if the number of turning in the transformers increased, there is an increase in resistance to the flow of current in them.