A potentiometer circuit has been set up for finding the internal resistance of a given cell. The main battery, used across the potentiometer wire, has an emf of $$2.0$$ V and a negligible internal resistance. The potentiometer wire itself is $$4$$ m long. When the resistance R, connected across the given cell, has values of (i) infinity (ii) $$9.5$$ Ω the balancing lengths on the potentiometer wire are found to be $$3$$ m and $$2.85$$ m, respectively. The value of internal resistance of the cell is

Question

A potentiometer circuit has been set up for finding the internal resistance of a given cell. The main battery, used across the potentiometer wire, has an emf of $$2.0$$ V and a negligible internal resistance. The potentiometer wire itself is $$4$$ m long. When the resistance R, connected across the given cell, has values of (i) infinity              (ii) $$9.5$$ Ω  the balancing lengths on the potentiometer wire are found to be $$3$$ m and $$2.85$$ m, respectively. The value of internal resistance of the cell is

Infinity Learn · Accepted Answer

The internal resistance of the cell is $$r=l1l2-1RHere$$, $$l1=3$$ m,$$l2=2.85$$ m,$$R=9.5$$Ω∴  $$r=32.85-1(9.5$$Ω$$)=0.152.85$$×$$9.5$$Ω$$=0.5$$Ω

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