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1

Tangent Galvanometer

Principle:

A magnetic needle is suspended so that two mutually perpendicular magnetic fields act on it; one due to a current carrying circular coil, and the other due to the earth's magnetic field (horizontal component B_{H}). The needle settles in a position given by tangent law: B = B_{H} tan q

Construction:

A T.G. consists of:

Settings:

(1) The instrument is levelled so that the magnetic needle is exactly horizontal (2) The coil is arranged in magnetic meridian.

The Two Magnetic Fields Acting on the Needle

(1) Field B due to current in the coil acts in East-West direction. (2) Field B_{H}, which is the horizontal component of earth's magnetic field; acts in North-South direction.

Formula

Magnetic field produced at the centre of the current careying by the coil is given by:

B =

m_{0} n I

2 r

where, B = magnetic field at the centre of the circular coil

I = current in the coil n = number of turns of the coil m_{0} = permeability of free space.

B = B_{H} tan q … by tangent law

\

= B_{H} tan q

\ I =

(

2 r B_{H}

)

tan q

m_{0} n

K =

is known as reduction factor.

\ I = K tan q

Sensitivity of T.G.

·

S =

d q

=

cos^{2}q

d I

K

\ Sensitivity increases

Accuracy of T.G.

Relative error in measurement of current I =

I

Taking I = K tan q and differentiating,

2 d q

sin 2 q

Accuracy is maximum when error is minimum. i.e., when sin 2q is maximum

Putting maximum value of sin 2q = 1

sin 2q = 1 2q = 90° q = 45°

Accuracy is maximum at q = 45°