In the circuit given below,if the bulb is to glow with maximum intensity,the value of $R$ is (neglect internal resistance of the cell) (in $\Omega$)

In the given circuit,the power generated in the $1 \, \Omega$ resistance will be maximum for $x$ equal to ................ $\Omega$.

Four identical electrical lamps are labelled $1.5\,V$,$0.5\,A$,which describes the condition necessary for them to operate at normal brightness. $A$ $12\,V$ battery of negligible internal resistance is connected to the lamps as shown. Then:

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?

$A$ cell of constant $e.m.f.$ is first connected to a resistance $R_1$ and then connected to a resistance $R_2$. If the power delivered in both cases is the same,then the internal resistance of the cell is:

The reading of the ideal voltmeter in the adjoining diagram will be ................. $V$.