When a resistance of $2\,\Omega$ is connected across the terminals of a cell,the current is $0.5\,A$. When the resistance is increased to $5\,\Omega$,the current is $0.25\,A$. The $e.m.f.$ of the cell is ................. $V$.

$A$ resistor is connected to a battery of $12 \text{ V}$ emf and internal resistance $2 \text{ }\Omega$. If the current in the circuit is $0.6 \text{ A}$, the terminal voltage of the battery is: (in $\text{ V}$)

$A$ uniform metallic wire having resistance $4 \ \Omega$ is bent to form a square loop $(ABCD)$ (see figure). $A$ resistance of $2 \ \Omega$ is connected between points $B$ and $D$ and a battery of $2 \ V$ is connected across points $A$ and $C$ as shown in the figure. Now the value of current $(I)$ is: (in $A$)

$A$ battery of $e.m.f.$ $10\, V$ and internal resistance $0.5\, \Omega$ is connected across a variable resistance $R$. The value of $R$ for which the power delivered in it is maximum is given by ......... $\Omega$.

In the following circuit, a power of $50 \ W$ is absorbed in the section $AB$ of the circuit. The value of resistance '$X$' is (in $\Omega$)

Resistances $R_1$ and $R_2$ are joined in parallel and a current is passed so that the amount of heat liberated is $H_1$ and $H_2$ respectively. The ratio $\frac{H_1}{H_2}$ has the value: