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Aug
The ability of production of induced emf in one coil due to varying current in the neighbouring coil is called mutual inductance. Let and be the no of turns it each solenoid of equal length l.
17Derive an expression for the self-inductance of a long air-cored solenoid of length and number of turns N.
Derive an expression for mutual inductance. Define mutual inductance between a pair of coils. Derive an expression for the mutual inductance of two long coaxial solenoids of same length wound one over the other. Where M is the constant of proportionality and is called the coefficient of mutual induction or mutual inductance of two coils.
The unit of mutual inductance is. M ф 2 T I fracWeberAmpere fracVolt-secAmpere Henry. The unit of M is Henry.
If I 1 ф 2 T M x 1 M ф 2 T. Thus the coefficient of mutual inductance of two coils is equal to the amount of. Similarly the mutual inductance between the two solenoids when current is passed through solenoid S 2 and induced emf is produced in solenoid S 1 is given by M12 μ 0n1n2Al M12 M21 M say Hence coefficient of mutual induction between the two long solenoids is given by.
Let and be the no of turns it each solenoid of equal length l. Therefore flux through each turn of solenoid is. The total flux through all the turns in a length l of is.
And we know that where M is the mutual inductance. Therefore mutual inductance of two long coaxial solenoids of same lenth is. B Derive an expression for the mutual inductance of two long co-axial solenoids of same length wound one over the other.
C In an experiment two coils C 1 and C 2 are placed close to each other. Find out the expression for the emf induced in the coil C 1. Mutual inductance between the two coils is equals to the magnetic flux linked with one coil when a unit current is passed in the other coil.
Alternatively e - MdIdt. Mutual inductance is equal to the induced emf set up in one coil when the rate of change of current flowing through the other coil is. A Define the term mutual inductance.
Deduce the expression for the mutual inductance of two long coaxial solenoids having different radii and different number of turns. B A coil is mechanically rotated with constant angular speed w in a uniform magnetic field which is perpendicular to the axis of rotation of the coil. The plane of the coil is initially held perpendicular to the field.
For determining the Mutual Inductance between the two coils the following expression is used. This expression is used when the magnitude of mutually induced emf in the coil and the rate of change of current in the neighbouring coil is known. If e m 1 volt and dI 1 dt 1 ampere then putting this value in the equation 1 we get the value of mutual inductance as M1 Henry.
This gives the expression for mutual inductance M21 of the solenoid 2 with respect to solenoid 1. Similarly we can find mutual inductance M12 of solenoid 1 with respect to solenoid 2 as given below. The magnetic field produced by the solenoid 2 when carrying a current i2 is B2 µ n2i2.
Thus we see that when the conductors of a 3-phase transmission line are not equidistant from each other ie unsymmetrically spaced the flux linkages and inductances of various phases are different which cause unequal voltage drops in the three phases and transfer of power between phases represented by imaginary terms of the expression for inductances due to mutual inductances even if the currents in. Derivation of Inductance For the DC source when the switch is ON ie. Just at t 0 a current starts flowing from its zero value to a certain value and with respect to time there will be a rate of change in current momentarily.
This current produces changing flux φ through the coil. The ability of production of induced emf in one coil due to varying current in the neighbouring coil is called mutual inductance. Magnetic flux PI MI Where M is called coefficient of mutual induction.
Mutual Inductance of Two Long Solenoids. Suppose a current i is passed through the inner solenoid. Let and be the no of turns it each solenoid of equal length l.
Therefore flux through each turn of solenoid is. The total flux through all the turns in a length l of is. And we know that where M is the mutual inductance.
If current is passed through C 2 then find an expression for mutual inductance between the two coils. All India 20092011 C. 17Derive an expression for the self-inductance of a long air-cored solenoid of length and number of turns N.
18Define mutual inductance and write its SI unit. Write the expression for the mutual inductance between a. The SI unit for inductance is the henry H.
11-3 1 henry1 H 1 Tm2A 1114 We shall see that the mutual inductanceM21depends only on the geometrical properties of the two coils such as the number of turns and the radii of the two coils.