NCERT Solutions for Chapter: Current Electricity, Exercise 3: SA

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 ‘$n$’ ?

Let there be n resistors$R_1........R_n$ with $R_{\max }=\max (R_1......R_n)$ and $R_{\min }=\min \{R_{\mathit{1}}.....R_{\mathit{n}}\}$. Show that when they are connected In parallel, the resultant resistance $R_p<R_{\min }$  and when they are connected In series, the resultant resistance $R_s>R_{\max }$. Interpret the result physically.

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 ?

Two conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter $1\mathrm{mm}$. Conductor B is a hollow tube of outer diameter $2\mathrm{mm}$ and inner diameter $1\mathrm{mm}$. Find the ratio of resistance ${\mathrm{R}}_{\mathrm{A}}$to ${\mathrm{R}}_{\mathrm{B}}$.

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.