Question

QN Figure shows use of potentiometer for comparision of two
resistances. The balance point with standard resistance R = 10ohm
is at 58.3 cm, while that with unknown resistance X is 68.5 cm. Find X.
10
58 3cm 68.5cm
A
B
R=1052
G
X
​

Answer 1

Step-by-step explanation:

Resistance of the standard resistor, R=10.0Ω

Balance point for this resistance, l

1

=58.3cm

Current in the potentiometer wire =i

Hence, potential drop across R, E

1

=iR

Resistance of the unknown resistor =X

Balance point for this resistor, l

2

=68.5cm

Hence, potential drop across X, E

2

=iX

The relation connecting emf and balance point is,

E

2

E

1

=

l

2

l

1

iX

iR

=

l

2

l

1

X=

l

2

l

1

×R

=

58.3

68.5

×10=11.749Ω

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

If we fail to find a balance point with the given cell of emf, ε, 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.