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Question

On interchanging, the resistances, the balance point of a meter bridge shifts to 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?
  1. 910 Ω
  2. 550 Ω
  3. 990 Ω
  4. 505 Ω


Solution

The correct option is B 550 Ω
Initial case-
R1(1000R1)=l(100l)
R1(100l)=l(1000R1)     ...(1)
Similarly, we can write
Final case -
R2R1=1000R1R1=l10110l
(1000R1)(110l)=(l10)R1     ...(2)
By solving equation (1) and equation (2), we get l=55 cm

Putting value of l in equation (1)
R1(10055)=55(1000R1)
45R1=5500055R1
100R1=55000
R1=550 Ω

On balancing condition
R1(100l)=(1000R2)l
On interchanging resistances

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