Question 309: Current Electricity

Question

In a circuit for finding the resistance of a galvanometer  by half deflection method,  a 6 V battery and a high resistance of 11 k$$\Omega $$ are used. The figure of merit of the galvanometer is 60 $$\mu A/$$division.  In the absence of shunt resistance, the galvanometer produces a deflection of $$	heta $$ = 9 divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of $$	heta /2,$$ is closest to :

Accepted Answer

Current required by unit deflection is 60 $$\mu$$A.
For, $$	heta$$ = 9 current is I = 9 $$	imes$$ 60 $$\mu$$A
$$\Rightarrow$$ I = 540 $$\mu$$A = 540 $$	imes$$ 10
$$-$$6
A
Let G is resistance of galvanometer. Then,
$$540 	imes {10^{ - 6}} = {6 \over {(11000 + G)}}$$
[11000 + G] 90 $$	imes$$ 10
$$-$$6
= 1
99000 + 9G = 10
5
9G = 100000 $$-$$ 99000
9G = 1000
$$G = {{1000} \over 9}\Omega $$
Also, in half deflection method,
$$G = {{RS} \over {R - S}} \Rightarrow {{1000} \over 9} = {{11000\,S} \over {11000 - S}}$$
$${1 \over 9} = {{11S} \over {11000 - S}} \Rightarrow 11000 - S = 99\,S$$
100 S = 11000 $$\Rightarrow$$ S = 110 $$\Omega$$

Answer

500 $$\Omega $$

Answer

220 $$\Omega $$

Answer

55 $$\Omega $$

Answer

110 $$\Omega $$

Current Electricity

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