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Question:

In a meter bridge, as shown in the figure, it is given that resistance Y = 12.5Ω and that the balance is obtained at a distance 39.5cm from end A (by jockey J). After interchanging the resistances X and Y, a new balance point is found at a distance l2 from end A. What are the values of X and l2?

8.16Ω and 60.5cm

19.15Ω and 60.5cm

8.16Ω and 39.5cm

19.15Ω and 39.5cm

Solution:

In a meter bridge, the balance condition is given by:

X/Y = l1/(100 - l1)

where X and Y are the resistances, and l1 is the balance point distance from end A.

Given: Y = 12.5Ω, l1 = 39.5cm

Initially:
X/12.5 = 39.5/(100 - 39.5)
X/12.5 = 39.5/60.5
X = (39.5/60.5) * 12.5
X = 8.16Ω

After interchanging X and Y:
Y/X = l2/(100 - l2)
12.5/8.16 = l2/(100 - l2)
1.53 = l2/(100 - l2)
153 - 1.53l2 = l2
153 = 2.53l2
l2 = 153/2.53
l2 = 60.5cm

Therefore, the values of X and l2 are 8.16Ω and 60.5cm respectively.