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MHT-CET : Physics Entrance Exam

MHT - CET : Physics - Magnetic Effect of Electric Current Page 1

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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 BH). The needle settles in a position given by tangent law: B = BH tan q

 

Construction:

 

A T.G. consists of:

  • A coil with a number of turns on a circular frame
  • The frame is fixed vertically on a horizontal base
  • A magnetic needle pivoted at the centre of the coil
  • Pointer fixed at right angles to the needle.

 

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 BH, 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 =

m0 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

m0 = permeability of free space.

 

B = BH tan q by tangent law

 

\ 

m0 n I

  = BH tan q

2 r

 

\ I =  

(

2 r BH

)

 tan q

m0 n

 

K =  

(

2 r BH

)

 is known as reduction factor.

m0 n

 

\ I = K tan q

 

 

 

Sensitivity of T.G.

 

  •  The sensitivity of a galvanometer is defined as the angle of deflection per unit current  passing through it.

 

S = 

d q

=

cos2q

d I

K

 

  •  For greater sensitivity, K must be small.

 

K = 

2 r BH

m0 n

 

 

\ Sensitivity increases

 

 

  1. if radius is reduced
  2. if effective value of BH is reduced.
  3. if number of turns are increased.

 

 

Accuracy of T.G.

 

 Relative error in measurement of current I =  

d I

I

 

 

 Taking I = K tan q and differentiating,

 

 

d I

=

2 d q

I

sin 2 q

 

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

 

 

 Putting maximum value of sin 2q = 1

 

sin 2q = 1
2
q = 90
q = 45

 

\ 

Accuracy is maximum at q = 45

 

 

 

 

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