Two cells of same emf but different internal resistances $I_{1}$ and $I_{2}$ are connected in series with a resistance $R$. The value of resistance $R$, for which the potential difference across second cell is zero, is
JEE MAIN 2022, Medium
Download our app for free and get started
$I=\frac{2 E }{R+I_{1}+I_{2}} \ldots \ldots( i )$
But $V _{ A }- V _{ B }= E - I _{2}=0$
$\Rightarrow I =\frac{ E }{ I _{2}} \quad \ldots \text { $(ii)$}$
Comparing values of $I$ from $(i)$ and $(ii)$
$\frac{E}{r_{2}}=\frac{2 E}{R+r_{1}+r_{2}}$
$\Rightarrow R=r_{2}-r_{1}$
Download our appand 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.*
Similar Questions
- 1A wire of resistance $R$ is bent to form a square $ABCD$ as shown in the figure. The effective resistance between $E$ and $C$ is ( $E$ is mid-point of arm $CD$ )View Solution
- 2A fuse wire with radius $1\, mm$ blows at $1.5\, amp$. The radius of the fuse wire of the same material to blow at $3\,A$ will beView Solution
- 3The heat produced by a $100\, watt$ heater in $2$ minute will be equal toView Solution
- 4Model a torch battery of length $l$ to be made up of a thin cylindrical bar of radius $'a'$ and a concentric thin cylindrical shell of radius ' $b$ ' fille in between with an electrolyte of resistivity $\rho$ (see figure). If the battery is connected to a resistance of value $R ,$ the maximum Joule heating in $R$ will take place forView Solution
- 5A wire of resistance $R$ is divided in $10$ equal parts. These parts are connected in parallel, the equivalent resistance of such connection will beView Solution
- 6When the current $i$ is flowing through a conductor, the drift velocity is $v$. If $2i$ current is flowed through the same metal but having double the area of cross-section, then the drift velocity will beView Solution
- 7Two wires '$A$' and '$B$' of the same material have their lengths in the ratio $1 : 2$ and radii in the ratio $2 : 1$. The two wires are connected in parallel across a battery. The ratio of the heat produced in '$A$' to the heat produced in '$B$' for the same time isView Solution
- 8View SolutionSensitivity of potentiometer can be increased by
- 9In the potentiometer circuit as shown in the figure, the balance length $Al = 60\ cm$ when switch $S$ is open. When switch $S$ is closed and the value of $R$ is $5W$ the balance length $Al' = 50 cm.$ The internal resistance of the cell $C'$ is : .............. $\Omega$View Solution
- 10For the circuit shown in the figure, the current $I$ will be .......$A$View Solution
