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?

In the diagram,the resistance between any two adjacent junctions is $R$. The equivalent resistance across terminals $A$ and $B$ is:

Two wires $A$ and $B$ made of the same material and having their lengths in the ratio $6 : 1$ are connected in series. The potential differences across the wires are $3\,V$ and $2\,V$ respectively. If $r_A$ and $r_B$ are the radii of $A$ and $B$ respectively,then $\frac{r_B}{r_A}$ is

When a cell is connected to a resistance of $2\,\Omega$,the current flowing is $0.5\,A$. When it is connected to a resistance of $5\,\Omega$,the current flowing is $0.25\,A$. What is the $emf$ of the cell in $volt$?

In the circuit shown,if a conducting wire is connected between points $A$ and $B,$ the current in this wire will

The internal resistances of two cells shown in the figure are $0.1\,\Omega$ and $0.3\,\Omega$. If $R = 0.2\,\Omega$,find the potential difference across the cells.