In a metre bridge experiment, resistances are connected as shown in figure. The balancing length `1_1` is 55 cm. Now an unknown resistance x is connected in series with P and the new balancing length is found to be 75 cm. The value of x is

Options

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

Answer

C

Explanation

For the given metre bridge `(P)/( Q) = (1_1)/(100-I_1)`
`I_1=55 cm" "100-l_1= 45 cm`
`therefore (3)/(Omega) = (55)/( 45) rArr Q = (27)/(11) Omega`
when x is connected in series with P,
`l_(1) = 75 cm, 100-l_(1) = 25 cm` then,
`(P+ x )/ (Q) = (75 cm)/(25 cm) , 3 + x = 3 xx (27)/(11) xx (48)/( 11) Omega`