Tuesday, 26 April 2016

Tangent galvanometer

Tangent galvanometer

Tangent  galvanometer  is a device used for measuring current. It works on the principle of tangent law. A magnetic needle suspended at a point where  there  are  two crossed fields at right angles to each other will come to rest in the direction of the resultant of the two fields.

Construction

It consists of a circular coil of wire wound over a non magnetic frame of brass or wood.The vertical frame is mounted on a horizontal circular turn table provided with three leveling screws. The vertical frame can be rotated about  its vertical diameter. There is a small upright projection at the center of  the turn table  on which a compass box is supported. The compass  box  consists  of  a  small  pivoted  magnet  to  which  a thin  long  aluminium  pointer  is  fixed  at  right  angles.  The  aluminium pointer can move over a circular scale graduated in degrees. The scale consists of four quadrants. The compass box is supported such that the center  of  the  pivoted  magnetic  needle  coincides  with  the  center  of  the coil.  Since  the  magnetic  field  at  the  center  of  the  coil  is  uniform  over a  very  small  area,  a  small  magnetic  needle  is  used  so  that  it  remains in an uniform field even in deflected position. Usually the coil consists of three sections of 2,5 and 50 turns, which are of different thickness, used  for  measuring  currents  of  different  strength.

Theory

When  the  plane  of  the  coil  is  placed  parallel  to  the  horizontal component of Earth’s magnetic induction and a current is passed  through  the  coil,  there  will  be  two  magnetic fields  acting  perpendicular  to  each  other (1) the  magnetic  induction  (B)  due  to  the  current in the coil acting normal to the plane of the coil and  (2)  the  horizontal  component  of  Earth’s magnetic  induction  (Bh),Due   to   these   two   crossed   fields,   the pivoted  magnetic  needle  is  deflected  through an  angle θ. According  to  tangent  Law,
B  =  Bhtanθ........(1)
If a current I passes through the coil of n turns and of radius a, the  magnetic  induction  at  the  center  of  the  coil  is
B  =  μnI/2a...........(2)
Substituting  equation  (2)  in  equation  (1)μnI/2a=  Bhtanθ
∴. I  =  (a2B/μn) *tan  θ
I  =  K tanθ...................(3)
where  K  = 2aBh/μn  is  called  the  reduction  factor  of  the  tangent galvanometer. It is a constant at a place. Using this equation, current in  the  circuit  can  be  determined. Since  the  tangent  galvanometer  is  most  sensitive  at  a  deflection of  45 degree, the  deflection  has  to  be  adjusted  to  be  between  30  and  60 degree.