Ratio of thermal energy released in two resistors $R$ and $3R$ connected in parallel in an electric circuit is:

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?

In the circuit element given here,if the potential at point $B$,$V_B = 0$,then the potentials of $A$ and $D$ are given as

In the following circuit,if $V_A - V_B = 6\,V$,then the value of resistance $R$ (in $\Omega$) is ............... $\Omega$.

In the circuit shown below,the power developed in the $6 \, \Omega$ resistor is $6 \, W$. The power in watts developed in the $4 \, \Omega$ resistor is

Water boils in an electric kettle in $15\,\text{min}$ after switching on. If the length of the heating wire is decreased to $2/3$ of its initial value,then the same amount of water will boil with the same supply voltage in ............. $\text{min}$.