One of the circuits for the measurement of resistance by potentiometer is shown. The galvanometer is connected at point A and zero deflection is observed at length PJ $$=$$ $$30$$ cm. In second case the secondary cell is changed.Take ES $$=$$ $$10$$ V and $$r=1$$ Ω in $$1st$$ reading and ES $$=$$ $$5$$ V and $$r=2$$ Ω in $$2nd$$ reading. In second case, the zero deflection is observed at length PJ $$=$$ $$10$$ cm. What is the resistance R (in$$ $$ohm)?

Question

One of the circuits for the measurement of resistance by potentiometer is shown. The galvanometer is connected at point A and zero deflection is observed at length PJ $$=$$ $$30$$ cm. In second case the secondary cell is changed.Take ES $$=$$ $$10$$ V and $$r=1$$  Ω in $$1st$$ reading and ES $$=$$ $$5$$ V and $$r=2$$  Ω in $$2nd$$ reading. In second case, the zero deflection is observed at length PJ $$=$$ $$10$$ cm. What is the resistance R (in$$ $$ohm)?

Infinity Learn · Accepted Answer

When there is no current through galvanometer, current through R $$isI=ESR+rPotential$$ difference $$=IR=ESRR+rNow$$ $$ESRR+r=KlFor$$ first case:  $$10$$ $$RR+1$$ $$=$$ $$K30$$                 ….(i)For$$ second case:  $$5$$ $$RR+2$$ $$=$$ $$K10$$          …..$$(ii)Dividing$$ $$(i) and (ii), we get R $$=$$ $$1$$  Ω

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