Figure shows a potentiometer circuit for comparison of two resistors. The balance point with a standard resistor R = 10.0 Ω is found to be 58.3 cm, while that with the unknown resistor 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?

Solution

Given, standard resistance, S=Y= 10 Ω
Balance point with standard resistor is obtained at, l₂= 58.3 cm
Balance point with unknown resistor is at, l₁= 68.5 cm
Unknown resistor is, R=X=?
Using the formula,
$\frac{R}{X} = \frac{l_{1}}{l_{2}}$

$\Rightarrow$ $X = R \frac{l_{1}}{l_{2}} = \frac{10 \times 68.5}{58.3} = 11.75 Ω$

If we fail to get a balance point with the given emf then, the potential drop across R and X are greater than the potential drop across the potentiometer wire AB. The obvious thing to do is to reduce the current in the outside circuit (i.e., the potential drop across R and X) suitably by putting a series resistor. Alternatively, we can increase the voltage of the driver cell inorder to increase the potential drop across the potentiometre wire.

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