a galvanometer serves as 2V full scale voltmeter when a 2500

a galvanometer serves as 2V full scale voltmeter when a 2500 ohm is used as amultiplier resistor and it serves as a 0.5A ammeter whena 0.22 ohm shunt resistor is used. determine the internal resistance of the galvanometer and the current required to produce full scale deflection

Solution

Ans) Given Vfsd=2 V Rm=2500 ohms

   Ifsd=0.5 A when Rsh=0.22 ohms

Let Ri = internal resistance of galvonometer and Ii= its full scale deflection current

When used as Voltmeter

Ii=Vfsd/(Ri+Rm)=2/(Ri+2500)

Ii*(Ri+2500)=2--------------equation1

When used as Ammeter

Ii=Ifsd*Rsh/(Rsh+Ri)=0.5*0.22/(0.22+Ri)

Ii*(0.22+Ri)=0.11

IiRi=0.11-0.22Ii -------------equation2

substituting equation 2 in equation1 we get

Ii*(Ri+2500)=2

Ii*Ri+2500Ii=2

0.11-0.22Ii+2500Ii=2

2499.78*Ii=2-0.11=1.89

Ii=1.89/2499.78=0.756 mA

Ii=0.756 mA (Galvonometer Full scale deflection current)

From equation 2

IiRi=0.11-0.22Ii

Ri=(0.11-0.22Ii)/Ii

Ri=145.27 ohms (internal resistance of Galvonometer)