In a meter bridge experiment to determine the value of unknown resistance, first the resistances 2Ω and 3Ω are connected in the left and right gaps of the bridge and the null point is obtained at a distance l cm from the left. Now when an unknown resistance xΩ is connected in parallel to 3Ω resistance, the null point is shifted by 10 cm to the right of wire. The value of unknown resistance x is ___

In a meter bridge experiment to determine the value of unknown resistance, first the resistances 2Ω and 3Ω are connected in the left and right gaps of the bridge and the null point is obtained at a distance l cm from the left. Now when an unknown resistance xΩ is connected in parallel to 3Ω resistance, the null point is shifted by 10 cm to the right of wire. The value of unknown resistance x is

Q. In a meter bridge experiment to determine the value of unknown resistance, first the resistances 2Ω and 3Ω are connected in the left and right gaps of the bridge and the null point is obtained at a distance l cm from the left. Now when an unknown resistance xΩ is connected in parallel to 3Ω resistance, the null point is shifted by 10 cm to the right of wire. The value of unknown resistance x is ____ Ω.

Correct Answer: 6

Explanation

In a meter bridge, the balance condition is:

R₁ / R₂ = l / (100 − l)

Initially,

R₁ = 2 Ω, R₂ = 3 Ω

So,

2 / 3 = l / (100 − l)

Solving,

2(100 − l) = 3l 200 − 2l = 3l 5l = 200 l = 40 cm

Now the null point shifts 10 cm to the right, so new balance length:

l′ = 40 + 10 = 50 cm

Now the resistance in the right gap is the parallel combination of 3 Ω and x Ω.

Equivalent resistance,

R = (3x) / (3 + x)

New balance condition:

2 / [(3x)/(3 + x)] = 50 / 50 = 1

So,

2 = (3x)/(3 + x)

2(3 + x) = 3x 6 + 2x = 3x x = 6

Hence, the value of the unknown resistance is 6 Ω.

Explanation

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