In the given circuit,the reading of the ideal voltmeter is $\frac{E}{2}$. Find the internal resistance $r$ of the cell in $\Omega$.

An electric bulb of $60 \, W, 120 \, V$ is to be connected to a $220 \, V$ source. What resistance should be connected in series with the bulb so that the bulb glows properly?

An infinite line charge of uniform electric charge density $\lambda$ lies along the axis of an electrically conducting infinite cylindrical shell of radius $R$. At time $t=0$,the space inside the cylinder is filled with a material of permittivity $\varepsilon$ and electrical conductivity $\sigma$. The electrical conduction in the material follows Ohm's law. Which one of the following graphs best describes the subsequent variation of the magnitude of current density $j(t)$ at any point in the material?

Inside a superconducting ring,six identical resistors each of resistance $R$ are connected as shown in the figure. Imagine a battery of $emf$ $E$ connected between points $O$ and $1$,with its positive terminal connected to $O$.

$A$ uniform metallic wire carries a current of $2\,A$ when a $3.4\,V$ battery is connected across it. The mass of the uniform metallic wire is $8.92 \times 10^{-3}\,kg$,its density is $8.92 \times 10^3\,kg/m^3$,and its resistivity is $1.7 \times 10^{-8}\,\Omega\cdot m$. The length of the wire is $l = \dots\dots\dots\dots\,m$.

Two electric bulbs whose resistances are in the ratio of $1 : 2$ are connected in parallel to a constant voltage source. The powers dissipated in them have the ratio: