In a meter bridge experiment, resistances are connected as shown in...

Given in the meter bridge,

In $I$ st case, $\dfrac{P}{Q} = \dfrac{{l}_{1}}{{l}_{2}}$

$⇒ \dfrac{4}{Q} = \dfrac{55}{100 - 55}$

$⇒ Q = \dfrac{4 \times 45}{55}$ ...(i)

In $2$ nd case, $\dfrac{P + x}{Q} = \dfrac{75}{25}$

$⇒ \dfrac{4 + x}{3} = Q$ ...(ii)

From Equations (i) and (ii), we get

$\dfrac{4 + x}{3} = \dfrac{36}{11}$

$4 + x = \dfrac{108}{11}$

$x = \dfrac{108 - 44}{11}$

$= \dfrac{64}{11}$

$⇒ 11x = 64$