$A$ student has $10$ resistors of resistance $r$. The minimum resistance made by him from given resistors is

Two wires of the same material and equal length are joined in parallel combination. If one of them has half the thickness of the other and the thinner wire has a resistance of $8\, \Omega$,the resistance of the combination is equal to

The equivalent resistance of the circuit shown in the figure is ............. $\Omega$

$A$ ring is made of a wire having a total resistance $R_0 = 12\,\Omega$. Find the ratio of the lengths $\frac{\ell_1}{\ell_2}$ of the two arcs between points $A$ and $B$ as shown in the figure,such that the equivalent resistance $R$ of the circuit between these points is $\frac{8}{3}\,\Omega$.

If three resistors of resistance $2 \,\Omega$,$4 \,\Omega$ and $5 \,\Omega$ are connected in parallel,then the total resistance of the combination will be:

In the given circuit,find the value of $V$. (in $V$)