Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

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 $\frac{dR}{dl} \alpha \frac{1}{\sqrt{l}}$ . Two equal resistances are connected as shown in the figure. The galvanometer has zero defelection when the jockey is at point P. What is is the length AP ?

Option 1)
0.3 m
Option 2)
0.25 m
Option 3)
0.2 m
Option 4)
0.35 m

Answers (1)

best_answer

Meter bridge -

$\frac{P}{Q}=\frac{R}{S}\Rightarrow S= \frac{(100-l)}{l}R$

- wherein

$AB=l$

$BC=(100-l)$

Given $\frac{dR}{dl}\alpha \frac{1}{\sqrt{l}}$

$\Rightarrow dR=k\left ( \frac{de}{\sqrt{l}} \right )$

k=constant

For zero deflection

$\frac{R^{1}}{R^{1}}=\frac{R_{1}}{R_{2}}=1$

$R_{1}=R_{2}$

$R_{1}=k\int_{0}^{l}\, \textrm{} \, \frac{dl}{\sqrt{l}}=k.2\sqrt{l}$

$R_{2}= k\int_{l}^{100-l} \, \frac{dl}{\sqrt{l}}=k(2-2\sqrt{l})$

$R_{1}=R_{2}$

$2k\sqrt{l}=k\left ( 2-2\sqrt{l} \right )$

$2\sqrt{l} \right=1$

$\sqrt{l}=\frac{1}{2}$

$l=\frac{1}{4}m$

or $l=25cm$

Option 1)

0.3 m

Option 2)
0.25 m
Option 3)

0.2 m

Option 4)

0.35 m

Posted by

admin

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JAC Chandigarh Counselling 2025: Round 1 seat allotment result out for BTech admissions

anam-khan

JoSAA round 5 seat allotment result 2025 out on josaa.nic.in

anam-khan

BTech aspirant from north-east or UT? Apply for CSAB NEUT counselling 2025 today

Latest Question