Question

coefficient of mutual inductance of for apair of coils and also give unit of mutual inductance

Answer 1

Answer:

Coefficient of Mutual Inductance

If orientation, size and shape of perimary coil C1​ and secondary coil C2​, remains same and in coil C1​ current is l1​, then second coil C2​ is related to magnetic-flux which is proportional to the flow of current i2​. i.e.,

ϕ2​∝l1​

or ϕ2​=Ml1​.........(1)

Here, M is proportionality constant, which is called mutual induction. Its value depend upon number of turns,area of secondary coil and medium.

If the current in coil C1​ changes with time, then flux linked with C2​,i.e.,ϕ2​ changes .

Thus, induced emf in coil C2​,

ε2​=−dtdϕ2​​

Thus, ε2​=−dtMdI1​​...............(2)

The negative sign in equation (2), indicate that the direction of induced emf in secondary coil opposes the growth or decay of current flow in a primary coil, from equation(1),

ϕ2​=Ml1​

If l1​=1Amp

then M=ϕ2​...........(2)

Thus the coefficient of mutual inductance is equal to the magnetic flux linked with secondary coil when the current flow in a primary coil is unity, from equation(2),

ε2​=MdtdI1​​

∴M=−dtdI1​​ε2​​,if−dtdI1​​=1

then m=ε2​

Hence the coefficient of mutual inductance is equal to the induced emf when decay rate of current in primary coil is unity.

The unit of mutual inductance

M=AmpWeber​ or henry (H)

=AmpereVolt×sec​=Volts−1A−1

The dimensional Formula

=DimentionofcurrentDimensionofmagneticflux​

=[A][MLT−2A−1]​=[MLT−2A−2]

Mutual inductance depends upon the number of turns in a coil, area of cross section and medium.

The S.I. unit of M is Wb/A or VA/A or henry (H) and its dimensions are [M1L2T−2A−2]