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 $.....d$.

Consider the circuit shown below where all resistors are $1 \,k\Omega$. If a current of magnitude $1 \,mA$ flows through the resistor marked $X$,the potential difference measured between points $P$ and $Q$ is ..............$V$.

$10$ resistors,each of resistance $10\,\Omega$,can be connected to obtain maximum and minimum equivalent resistance. The ratio of maximum to minimum equivalent resistance will be $..........$.

$A$ copper wire of radius $r$ and length $\ell$ is coated with a nickel layer until its radius becomes $2r$. If the resistivities of copper and nickel are $\rho_c$ and $\rho_n$ respectively,find the equivalent resistance of the wire.

$6 \Omega$ and $12 \Omega$ resistors are connected in parallel. This combination is connected in series with a $10 \text{ V}$ battery and a $6 \Omega$ resistor. What is the potential difference between the terminals of the $12 \Omega$ resistor (in $\text{ V}$)?

Four wires $AB, BC, CD, DA$ of resistance $4\, \Omega$ each and a fifth wire $BD$ of resistance $8\, \Omega$ are joined to form a rectangle $ABCD$,where $BD$ is a diagonal. The effective resistance between the points $A$ and $B$ is: