Two cells of emf $2\, E$ and $E$ with internal resistance $r _{1}$ and $r _{2}$ respectively are connected in series to an external resistor $R$ (see $figure$). The value of $R ,$ at which the potential difference across the terminals of the first cell becomes zero is
A$r _{1}+ r _{2}$
B$\frac{ r _{1}}{2}- r _{2}$
C$\frac{ r _{1}}{2}+ r _{2}$
D$r _{1}- r _{2}$
JEE MAIN 2021, Diffcult
Download our app for free and get started
B$\frac{ r _{1}}{2}- r _{2}$
b $i =\frac{3 E }{ R + r _{1}+ r _{2}}$
$TPD =2 E - ir _{1}=0$
$2 E = ir _{1}$
$2 E =\frac{3 E \times r _{1}}{ R + r _{1}+ r _{2}}$
$2 R +2 r _{1}+2 r _{2}=3 r _{1}$
$R =\frac{ r _{1}}{2}- r _{2}$
Download our app
and get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Suppose a current carrying wire has a cross-sectional area that, gradually become smaller along the wire, has the shape of a very long cone as shown in figure. Choose the correct statement
Water boils in an electric kettle in $15\,\min$ after switching on. If the length of the heating wire is decreased to $2/3$ of its initial value, then the same amount of water will boil with the same supply voltage in ............. $min$