Question
On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is 1 kΩ. How much was the resistance on the left slot before interchanging the resistances?
910Ω
990Ω
505Ω
550 Ω
Solution
D.
550 Ω
R1 + R2 = 1000
⇒ R2 = 1000-R1
On blancing condition
R1(100 - ℓ) = (1000-R1)ℓ ... (1)
on Inter-changing resistance
On balancing condition
(1000-R1)(110-ℓ) = R1(ℓ-10)
Or
R1(ℓ-10)=(1000-R1)(110-ℓ)....(2)
divide equation (1) / (2)
⇒ (100 -ℓ)(110 -ℓ) = ℓ(ℓ-10)
⇒ 11000 - 100ℓ -110 ℓ + ℓ2 = ℓ2-10ℓ
⇒ 11000 = 200ℓ
ℓ = 55
put in eq (1)
R1(100-55) = (1000-R1)55
R1(45) = (1000-R1)55
R1(9) = (1000-R1)11
20R1 = 11000
R1 = 550
