Three resistances of magnitude $2\,\Omega$,$3\,\Omega$,and $5\,\Omega$ are connected in parallel to a battery of $10\,V$ and of negligible resistance. The potential difference across the $3\,\Omega$ resistance will be ............... $V$.

Eight copper wires of length $l$ and diameter $d$ are joined in parallel to form a single composite conductor of resistance $R$. If a single copper wire of length $2\,l$ has the same resistance $R$,then its diameter will be $.....d$.

$(a)$ Three resistors $1 \;\Omega, 2 \;\Omega$ and $3 \;\Omega$ are combined in series. What is the total resistance of the combination?
$(b)$ If the combination is connected to a battery of $emf \; 12 \; V$ and negligible internal resistance,obtain the potential drop across each resistor.

$A$ wire of resistance $12 \,\Omega$ is bent into a circle. What is the equivalent resistance between two diametrically opposite points in $\Omega$?

For the shown circuit,find the effective resistance between the points $A$ and $B$.

You are given several identical resistances each of value $R = 10\,\Omega$ and each capable of carrying a maximum current of $1\,A$. It is required to make a suitable combination of these resistances to produce a resistance of $5\,\Omega$ which can carry a current of $4\,A$. The minimum number of resistances of the type $R$ that will be required for this job is: