JEE PYQ: Current Electricity Question 75
Question 75 - 2019 (12 Jan 2019 Shift 2)
In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that, the variation $\frac{dR}{dl}$ of its resistance R with length $l$ is $\frac{dR}{dl} \propto \frac{1}{\sqrt{l}}$. Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP?
(1) 0.2 m
(2) 0.3 m
(3) 0.25 m
(4) 0.35 m
Show Answer
Answer: (3)
Solution
$dR = k \frac{dl}{\sqrt{l}}$. $R_1 = k\int_0^l l^{-1/2},dl = k \cdot 2\sqrt{l}$. $R_2 = k\int_l^1 l^{-1/2},dl = k(2 - 2\sqrt{l})$. For balance: $R_1 = R_2$, $2\sqrt{l} = 2 - 2\sqrt{l}$, $4\sqrt{l} = 2$, $\sqrt{l} = 1/2$, $l = 1/4 = 0.25$ m.
BETA
