Two unknown resistances are connected in two gaps of a meter-bridge. The null point is obtained at 40 cm from the left end. A 30 Ω resistance is connected in series with the smaller of the two resistances, the null point shifts by 20 cm to

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Two unknown resistances are connected in two gaps of a meter-bridge. The null point is obtained at 40 cm from the left end. A 30 Ω resistance is connected in series with the smaller of the two resistances, the null point shifts by 20 cm to the right end. The value of smaller resistance in Ω is

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Correct answer: 24

l x = 40 cm , l R = 60 cm x R = l x l R = 40 60 = 2 3 ....... (i) ∴ x + 30 R = 60 40 = 3 2 ∴ x + 30 R = 3 2 ∴ 2x + 30 = 3 R R = 2 ( x + 30 ) 3 ........ (ii) From (i) and (ii), x2 x + 30 3 = 2 3 3 x 2 ( x + 30 ) = 2 3 9 x = 4 x + 120 5 x = 120 ⇒ x = 24 Ω

Two unknown resistances are connected in two gaps of a meter-bridge. The null point is obtained at 40 cm from the left end. A 30 Ω resistance is connected in series with the smaller of the two resistances, the null point shifts by 20 cm to the right end. The value of smaller resistance in Ω is

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