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. `54/12 Omega`
B. `20/11 Omega`
C. `48/11 Omega`
D. `11/48 Omega`

Answer

C

Explanation

For the given meter bridge
`P/Q = I_(1)/(100 - I_(1)`
`I_(1) = 55 cm rArr 100 - I_(1) = 45 cm`
`therefore P = 3Q`
`rArr Q = 3 xx 45/55 = 3 xx 9/11 = 27/11 Omega`
When x is connected in series with `P, l_(1) = 75 cm`
`rArr (P + x)/Q = (75 cm)/(25 cm) rArr 3 + x = 3 xx 27/11`
`rArr x = 81/11 -3 rArr x = 48/11 Omega`