In a meter bridge experiment, resistances are connected as shown in figure. The balancing length `l_(1)=55cm`. Now, an unknown resistance x is connected in series with P and the new balancing length is found to be 75 cm. What is the value of The value of 11x (in ohm)? (Given, `P=4Omega`)

Options

A. `(54)/(13)Omega`
B. `(20)/(11)Omega`
C. `(48)/(11) Omega`
D. `(11)/(48)Omega`

Answer

C

Explanation

For the balance point of meterbridge.
Case-I, when balancing length is 55 cm
`(P)/(Q) =(l_(1))/(100-l_(1)) rArr (3)/(Q)=(55)/(45)`
`Q=(45)/(55)xx 3" " ….(1)`
case - II When an unknown resistance x is involved
`(P+x)/(Q)=(l_(1))/(100-l_(1))`
`(3+x)/(Q)=(75)/(25) rArr 3+x =(75)/(25)xx Q" "....(2)`
By putting value of Q from equation (1) in equation (2)
`3+x=(75)/(25) xx (45xx3)/(55)`
`x=(81)/(11)-3= (81-33)/(11)=(48)/(11)Omega`