Question 222: Magnetism and Matter

Question

To know the resistance G of a galvanometer by half deflection method, a battery of emf VE and resistance R is used to deflect the galvanometer by angle $$	heta $$. If a shunt of resistance S is needed to get half deflection then G, R and S are related by the equation :

Accepted Answer

When only galvanometer G is present with the resistance R,
Here I
G
= $${{{V_E}} \over {R + G}}$$
When shunt  of resistance S is connected parallel to galvanometer,
Here I = $${{{V_E}} \over {R + {{GS} \over {G + S}}}}$$
As deflection is half, here current through galvanometer,
I
G
' = $${{{{m I}_G}} \over 2}$$
As both Galvanometer and shunt are parallel then potential are parallel then potential difference same.
$$ 	herefore $$   I
G
' (G) = (I $$-$$ I
G
'
)S
$$ \Rightarrow $$   I'
G
(G + S) = IS
$$ \Rightarrow $$   $${{{{m I}_G}} \over 2}$$ = $${{{m I}S} \over {G + S}}$$
$$ \Rightarrow $$   $${{{V_E}} \over {2\left( {R + G} ight)}}$$ = $${{{V_E}} \over {R + {{GS} \over {G + S}}}}$$ $$ 	imes $$ $${S \over {\left( {G + S} ight)}}$$
$$ \Rightarrow $$   $${1 \over {2\left( {R + G} ight)}}$$  =  $${{G + S} \over {R(G + S) + GS}}$$  $$ 	imes $$ $${S \over {\left( {G + S} ight)}}$$
$$ \Rightarrow $$   RG + RS + GS = 2RS + 2GS
$$ \Rightarrow $$   RG = RS + GS
$$ \Rightarrow $$    S(R + G) = RG

Answer

2S (R + G) = RG

Answer

S (R + G) = RG

Answer

2S = G

Answer

2G = S

Magnetism and Matter

To know the resistance G of a galvanometer by half deflection method, a battery of emf VE and resistance R is used to deflect the galvanometer by angle $\theta $. If a shunt of resistance S is needed to get half deflection then G, R and S are related by the equation :

Choose the correct answer: