Figure 3-34 shows a potentiometer circuit for comparison of two resistances- The balance point with a standard resistor R -10-0 - 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 - -

Given: The balance point for a standard resistor R=10.0 #x2009; #x03A9; is 58.3 #x2009;cm and the balance point for unknown resistance X i ...

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Standard X

Physics

Combination of Resistors

Figure 3.34 s...

Question

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 ?

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Solution

Given: The balance point for a standard resistor R=10.0 Ω is 58.3 cm and the balance point for unknown resistance X is 68.5 cm.

Consider the given figure.

The emf in terms of balance point is given as,

ε=ϕl

Where, ϕ is the potential drop per unit length and l is the length of the wire.

Therefore, we can write,

ε 1 ε 2 = l 1 l 2 iR iX = l 1 l 2 X=R× l 2 l 1

By substituting the given values in the above expression, we get

X= 68.5 58.3 ×10 ≈11.75 Ω

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

According to the question, if we fail to find a balance point, a resistance is connected in series with it to reduce the potential drop across the R and X. Because to obtain the balance point, potential drop across R or X should be smaller than the potential drop across the potentiometer wire AB.

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