If the galvanometer in the circuit (Fig.) reads zero, find the value of resistor $\mathrm{R}$. The $12 \mathrm{V}$ source has negligible internal resistance. If cool air is blown across the wire wound resistance, what effect will be noticed and why ?

 As shown in Fig. , A and B are two points on a uniform ring of resistance $\mathrm{R}.$ If the part $\mathrm{AB}$ of the ring subtends an angle $\mathrm{\theta }$ at the centre $\mathrm{C}$ of the ring, find the equivalent resistance of the ring between the points $\mathrm{A}$ and $\mathrm{B}.$

A cell of unknown emf $\epsilon$ and internal resistance r, two unknown resistances ${\mathrm{R}}_1$ and ${\mathrm{R}}_2\left({\mathrm{R}}_2>{\mathrm{R}}_1\right)$ and a perfect ammeter are given. The current in the circuit is measured in five different situations:

Without any external resistance in the circuit

The current obtained in the five cases are :

$0.42 \mathrm{A}, 0.6 \mathrm{A}, 1.05 \mathrm{A}, 1.4 \mathrm{A}$, and $4.2 \mathrm{A}$

but not necessarily in that order. Identify the currents in the five cases listed above and calculate $\mathrm{E}, \mathrm{r}, {\mathrm{R}}_1$ and ${\mathrm{R}}_2$.