$10$ resistors,each of resistance $R$,are connected in series to a battery of $emf$ $E$ and negligible internal resistance. When those are connected in parallel to the same battery,the current is increased $n$ times. The value of $n$ is:

Write the equation for the equivalent resistance of $n$ resistors connected in series and the equation for the equivalent resistance of $n$ resistors connected in parallel.

Two bulbs of $100\, W, 220\, V$ and $200\, W, 220\, V$ are connected in series to a $220\, V$ supply. What is the total power consumed in $W$?

$A$ Copper $(Cu)$ rod of length $25 \, cm$ and cross-sectional area $3 \, mm^2$ is joined with a similar Aluminium $(Al)$ rod as shown in the figure. Find the resistance of the combination between the ends $A$ and $B$ (in $m\Omega$).
(Take Resistivity of Copper $= 1.7 \times 10^{-8} \, \Omega \cdot m$,Resistivity of Aluminium $= 2.6 \times 10^{-8} \, \Omega \cdot m$)

Find the equivalent resistance between the points $a$ and $b$.

$A$ 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 $\frac{8}{3}\,\Omega$.