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  4. The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of 15 Ω resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of 10 V is maintained across AC . <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/596909a74b39f98a777d333607abe3b7-.png />

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Q. The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of $15\, \Omega$ resistance is connected across $BD$. Calculate the current through the galvanometer when a potential difference of $10 \,V$ is maintained across $AC .$
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JEE MainJEE Main 2021Current Electricity

Solution:

image
$\frac{x-10}{100}+\frac{x-y}{15}+\frac{x-0}{10}=0$
$53 \,x-20\,y=30 \ldots . .(1)$
$\frac{y-10}{60}+\frac{y-x}{15}+\frac{y-0}{5}=0$
$17\,y-4 \,=10 \ldots \ldots(2)$
on solving $(1) \&(2)$
$x=0.865$
$y=0.792$
$\Delta V=0.073\,R=15 \Omega$
$i=4.87\,mA$