In figure, AB is a potentiometer wire, length 10 m and resistance `2 Omega` with open the balancing length is 5.5 m. However, on closing key K the balancing length reduces to 5 m. The initial resistance of the cell `E_(1)` is

Options

A. `0.01 Omega`
B. `0.1 Omega`
C. `0.2 Omega`
D. `1 Omega`

Answer

B

Explanation

`l_(AB)=10m, R_(AB)=2 Omega, R_(AJ)=1 Omega`
` E_(1)=rho L` (When key is open)
`E_(1)=rhoxx5.5 implies V_(1)=5rho`
`(E-V)/(V) R=r(5.5rho-5rho)/(5rho)xx1=r(0.5)/(5)xx1=r`
` r=0.1 Omega`