Figure 3.34 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 ε?
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, ε, then the potential drop across R and Xmust 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.