The total current supplied by the battery to the circuit is ............ $A$.

In the given circuit,if the current through the $10 \Omega$ resistor is $2.5 \text{ A}$,the value of $R$ is . . . . . . . (in $\Omega$)

$A$ $5\, V$ battery with internal resistance $2\, \Omega$ and a $2\, V$ battery with internal resistance $1\, \Omega$ are connected to a $10\, \Omega$ resistor as shown in the figure. The current in the $10\, \Omega$ resistor is:

Two resistances,each equal to $R_0$ at $0\,^oC$,have temperature coefficients of resistance $\alpha_1$ and $\alpha_2$. When they are joined in series,the temperature coefficient of the equivalent resistance is:

Three identical batteries are connected in series with a wire of length $L$. The temperature of the wire increases by $T$ in time $t$. If $N$ such batteries are connected in series with a wire of the same material but length $2L$,the temperature increases by the same amount $T$ in the same time $t$. Find the value of $N$.

Two sources of equal $emf$ $E$ are connected in series to an external resistance $R$. The internal resistances of the two sources are $R_1$ and $R_2$ $(R_2 > R_1)$. If the potential difference across the source having internal resistance $R_2$ is zero,then: