An Unknown Resistance R1 is Connected in Series

Answer: B. 20 ohms

An unknown resistance R_1​ is connected in series with a resistance of 10Ω. This combination is connected to one gap of a meter bridge while a resistance R₂​ is connected to the other gap. The balance point is at 50 cm. Now when the 10Ω resistance is removed, the balance point shifts to 40 cm. The value of R_1​ is (in ohms):20 ohms.

Solution:

Given an unknown resistance, R1​ is connected in series with a resistance of 10Ω .

The balance point l₁=50 cm

it is a meter bridge, 

so l₁+l₂=100 cm

 l₂=100-l₁=50 cm

(R₁+10)/R₂=l₁/l₂=l₁/(100-l₁)

(R₁+10)/R₂=50/(100-50)

R₁+10=R₂________(1)

When the 10-ohm resistor is removed, The balance point l₁=40 cm.

l₂=100-l₁=100-40=60

R₁/R₂=l₁/l₂=40/60

R₁=2/3R₂ _________(2)

By solving equations (1) &(2)

R₁=20 Ohms

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