In the given circuit, an ideal voltmeter connected across the $10\,\Omega $ resistance reads $2\, V$. The internal resistance $r$, of each cell is ................... $\Omega$
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Two resistances ${R_1}$ and ${R_2}$ are made of different materials. The temperature coefficient of the material of ${R_1}$ is $\alpha $ and of the material of ${R_2}$ is $ - \beta $. The resistance of the series combination of ${R_1}$ and ${R_2}$ will not change with temperature, if ${R_1}/{R_2}$ equals
Current $l$ versus time $t$ graph through a conductor is shown in the figure. Average current through the conductor in the interval $0$ to $15 \,s$ is ............ $A$
In a potentiometer arrangement, a cell of emf $1.20\, V$ gives a balance point at $36\, cm$ length of wire. This cell is now replaced by another cell of emf $1.80\, V$. The difference in balancing length of potentiometer wire in above conditions will be $....cm$.
A wire of resistance $x$ ohm is drawn out, so that its length is increased to twice its original length, and its new resistance becomes $20 \,\Omega$, then $x$ will be ........ $\Omega$
When two identical batteries of internal resistance $1 \Omega$ each are connected in series across a resistor $\mathrm{R}$, the rate of heat produced in $R$ is $J_1$. When the same batteries are connected in parallel across $R$, the rate is $\mathrm{J}_2$. If $\mathrm{J}_1=2.25 \mathrm{~J}_2$ then the value of $\mathrm{R}$ in $\Omega$ is
A wire of resistor $R$ is bent into a circular ring of radius $r$. Equivalent resistance between two points $X$ and $Y$ on its circumference, when angle $XOY$ is $\alpha$, can be given by