First a set of $n$ equal resistors of $R \Omega$ each are connected In series to a battery of emf $E$ and Internal resistance $R$. A current $I$ Is observed to flow. Then the $n$  resistors are connected in parallel to the same battery. It is observed that the current is increased $10$times. What is ‘$n$’ ?

The circuit in Figure shows two cells connected In opposition to each other. Cell $E_1$ is of emf $6\mathrm{V}$ and Internal resistance $2\mathrm{\Omega }$; the cell $E_2$ is of emf $4\mathrm{V}$ and Internal resistance $8\mathrm{\Omega }$. Find the potential difference between the points A and B.

Two cells of same emf $\mathrm{E}$ but internal resistance $r_1$; and $r_2$ are connected in series to an external resistor $R$(Figure)What should be the value of $R$so that the potential difference across the terminals of the first cell becomes zero ?

Suppose there is a circuit consisting of only resistances and batteries and we have to double (or increase it to $n$-times) all voltages and all resistances. Show that currents are unaltered. Do this for the given circuit.

Two cells of voltage $10 \mathrm{V}$ and $2\mathrm{V}$ and Internal resistances $10 \mathrm{\Omega } ,5 \mathrm{\Omega }$. respectively, are connected In parallel with the positive end of $10\mathrm{V}$battery connected to negative pole of $2\mathrm{V}$ battery (Figure). Find the effective voltage and effective resistance of the combination.

A room has AC run for $5$ hours a day at a voltage of $220\mathrm{V}$. The wiring of the room consists of $\mathrm{Cu}$ of $1 \mathrm{mm}$ radius and a length of $10 \mathrm{m}$. Power consumption per day is $10$ commercial units. What fraction of it goes in the Joule heating in wires? What would happen if the wiring is made of aluminum of the same dimensions?

$$\begin{gathered} {\rho }_{cu}= 1.7\times {10}^{-8} \Omega m \\ {\rho }_{Al}=2.7 \times {10}^{-8} \Omega m \end{gathered}$$

In an experiment with a potentiometer, ${\mathrm{V}}_{\mathrm{B}}= 10\mathrm{V}$. $R$ is adjusted to be $50\mathrm{\Omega }$ (Figure). A student wanting to measure voltage $E_1$, of a battery (approx.$8\mathrm{V}$) finds no null point possible. He then diminishes $R$ to $10\mathrm{\Omega }$ and Is able to locate the null point on the last ($4^{\mathrm{th}}$) segment of the potentiometer. Find the resistance of the potentiometer wire and potential drop per unit length across the wire in the second case.