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Question
When an unknown resistance 'X' is connected in the left gap of a meter bridge and a known resistance 'R' in the right gap, a null point is obtained at 40 cm from the left end. If a 2 Ω resistance is connected in series with 'X' the null point shifts towards the right by 10 cm, with some resistance in the right gap. The value of 'X' must be ______
Options
4Ω
2Ω
3Ω
1Ω
Solution
When an unknown resistance 'X' is connected in the left gap of a meter bridge and a known resistance 'R' in the right gap, a null point is obtained at 40 cm from the left end. If a 2 Ω resistance is connected in series with 'X' the null point shifts towards the right by 10 cm, with some resistance in the right gap. The value of 'X' must be 4Ω.
Explanation:
`X/R = 40/60 = 2/3 ⇒ X = (2R)/3`
∴ R = `(3X)/2`
`(X + 2)/R = 50/50 = 1`
∴ X + 2 = R
X + 2 = `(3X)/2`
0.5X = 2
∴ X = 4Ω
