It takes $15 \ min$ to heat water in an electric kettle. If the length of the heating coil is reduced to $2/3$ of its original length,how many minutes will it take to heat the same amount of water?

The potential difference $(V_A - V_B)$ between the points $A$ and $B$ in the given figure is ............ $V$.

$A$ wire of cross-section area $A$,length $L_1$,resistivity $\rho_1$ and temperature coefficient of resistivity $\alpha_1$ is connected to a second wire of length $L_2$,resistivity $\rho_2$,temperature coefficient of resistivity $\alpha_2$ and the same area $A$,so that the wires carry the same current. The total resistance $R$ is independent of temperature for small temperature changes if (Thermal expansion effect is negligible):

$A$ student was trying to construct the circuit shown in the figure below marked $(a)$,but ended up constructing the circuit marked $(b)$. Realising her mistake,she corrected the circuit,but to her surprise,the output voltage (across $R$) did not change. The value of resistance $R$ is ............ $\Omega$

As shown,the circuit is made of $8$ different resistors. It is found that when $R_1 = 4\,\,\Omega,$ the resistance between $A$ and $B$ is $2\,\,\Omega.$ Now replace $R_1$ by a $6\,\,\Omega$ resistor,what is the resistance between $A$ and $B$?

When a potential difference $V$ is applied across a wire of resistance $R$,it dissipates energy at a rate $W$. If the wire is cut into two halves and these halves are connected in parallel across the same supply,the energy dissipation rate will become: