Class 12 Physics - Chapter Current Electricity NCERT Solutions | Figure shows a potentiometer circuit for

Welcome to the NCERT Solutions for Class 12th Physics - Chapter Current Electricity. This page offers a step-by-step solution to the specific question from Excercise ".$ex_no." , Question 23: figure shows a potentiometer circuit for compariso....
Question 23

Figure shows a potentiometer circuit for comparison of two resistances. The balance point with a standard resistor R = 10.0 Ω  is found to be 58.3 cm, while that with the unknown resistance X is 68.5 cm. Determine the value of X. What might you do if you failed to find a balance point with the given cell of emf Ω µ?

Answer

Resistance of the standard resistor, R = 10.0 Ω 

Balance point for this resistance, l1 = 58.3 cm

Current in the potentiometer wire = i

Hence, potential drop across R, E1 = iR

Resistance of the unknown resistor = X

Balance point for this resistor, l2 = 68.5 cm

Hence, potential drop across X, E2 = iX

The relation connecting emf and balance point is,

Therefore, the value of the unknown resistance, X, is 11.75 Ω .

If we fail to find a balance point with the given cell of emf, Ωµ, then the potential drop across R and X must be reduced by putting a resistance in series with it. Only if the potential drop across R or X is smaller than the potential drop across the potentiometer wire AB, a balance point is obtained.

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