If the power dissipated in the circuit is $150\,W,$ then the value of $R$ is ............... $\Omega$.

The equivalent resistance between the adjacent corners of a regular $n$-sided polygon made of a uniform wire of total resistance $R$ is:

If you are provided a set of resistances $2\, \Omega, 4\, \Omega, 6\, \Omega$ and $8\, \Omega$. Connect these resistances so as to obtain an equivalent resistance of $\frac{46}{3}\, \Omega$.

The effective resistance between $A$ and $B$ in the figure is $\frac{7}{12} \Omega$ if each side of the cube has $1 \Omega$ resistance. The effective resistance between the same two points, when the link $A B$ is removed, is

Five identical electric filament lamps numbered $1$ to $5$ are joined in parallel across an ideal source as shown in the figure. When all the bulbs are working, the reading in the ammeter is $3 \,A$. When lamp '$1$' is switched off, the reading of the ammeter is (in $\,A$)

The resistance of the series combination of two identical resistors is $S$. When they are joined in parallel,the total resistance is $P$. If $S = nP$,then the minimum possible value of $n$ is