## Determination Of Self Induction

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# Determination of Self- Induction by Raleigh’s method

The coil, whose self-inductance L is to be connected in the fourth arm of a Wheat stone’s bridge plug key K

_{3}is connected across r so that it may be short-circuited. P, Q and R are non-inductive resistances.

(a) Initially, K

_{3}is kept closed. The ohmic resistance S of the inductance coil alone is included in the fourth arm. P is made equal to Q. Then R is adjusted for no deflection in the B.G., by first pressing battery key K

_{1}and then galvanometer key K

_{2}. Under this condition, no current flows through the galvanometer.

(b) If now the galvanometer key2 is closed first and then the battery key K

_{1}, then a throw θ

_{1}is observed in the galvanometer. This throw arises due to an extra emf L di/dt induced in the coil while the current is growing. If G is galvanometer resistance, then current through it due to induced emf is

i’ = kL /G di /dt

Where k is constant which depends upon the relative resistance in the circuit.

Hence the total charge passing through the galvanometer, as the current in the coil grows from zero to a steady maximum value i0 is given by

q = ∫

^{i}

_{0}I dt = kL /G ∫

^{i}

_{0}di/ dt dt = kL /G i

_{0}______________________________… (1)

If θ1 be the first throw of the galvanometer, then,

Q = K θ

_{1}(1 + λ /2) _________________________________________________ … (2)

. : kL/G i

_{0}= K θ

_{1}[1 + λ /2] ____________________________________ (from 1 and 2)

= T/2π C /nBA. θ

_{1}[1 + λ /2]

(c) To eliminate k and i0, the key K

_{3}is opened and the resistance r is included in the arm CD. As r is small, it does not affect the current i0 in the arm CD appreciably. But it will introduce an additional emf ri

_{0}in the arm CD: This causes a steady current (Kr/G)i

_{0}through the galvanometer. K

_{1}is closed first and then K

_{2}. The steady deflection Φ in the galvanometer is noted. Then,

(kr /G) i

_{0}= C /nBA Φ.

Here, C /nAB is the current reduction factor of the galvanometer.

Dividing (3) by (4),

L /r = T /2π θ

_{1}/ Φ [1 + λ/2]

Or L = rT /2π θ

_{1}/ Φ [1 + λ/2]

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