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Question
Two resistances are connected in the two gaps of a meter bridge. The balance points is 20 cm from the zero end. When resistance of 15 ohm is connected in series with the smaller of the two resistances, the null point shifts to 40 cm. The smaller of the two resistances has the value (in ohm) ______.
Options
8
10
9
12
Solution
Two resistances are connected in the two gaps of a meter bridge. The balance points is 20 cm from the zero end. When resistance of 15 ohm is connected in series with the smaller of the two resistances, the null point shifts to 40 cm. The smaller of the two resistances has the value (in ohm) 9.
Explanation:
Let the resistances be P and Q. When balanced,
`"P"/"Q" = 20/80 = 1/4` ....(1)
When another resistance is connected in series,
`("P + 15")/"Q" = 40/60 = 2/3` ....(2)
From (i) and (ii),
`("P + 15")/"4P" = 2/3`
⇒ 3P + 45 = 8P
⇒ 5P = 45
⇒ P = 9 Ω
