Answer :

Concepts/Formula used:


Ohm’s Law:


Potential Difference (V) across a resistor of resistance R when current I passes through it is given by Ohm’s law:



Let the area of cross section of the wire (resistor) be A and resistivity be ρ.


Then,



Kirchhoff’s loop rule:


The sum of potential differences around a closed loop is zero.


(a)


We consider the circuit when there is no deflection:



Applying Kirchhoff’s rule on loop ABCF,




Using ,






Let the area of cross section of wire be A and resistivity be ρ.


Then,



where V is the voltage across a wire segment of length l.


As, all the quantities except for length are the same for all sections of wire AB,



Hence,





(b)


Let the current coming out of the main battery be I1 and the current through the galvanometer be I2.



Let the area of cross section of wire be A and resistivity be ρ.


Then,



where V is the voltage across a wire segment of length l.


As, all the quantities except for length are the same for all sections of wire AB,



Hence,



Using



Now, RAD and RDB are in series.





Applying Kirchhoff’s rule on loop ABCFA,






  ……………(1)


Applying Kirchhoff’s rule on loop ADEFA,







    ………………(2)

From (i) and (ii)




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