Physics - Magnetism Question with Solution | TestHub

Magnetic fields at the centre of the coils are equal. $$\therefore \frac{{\mu }_0{I}_1}{2r_1}=\frac{{\mu }_0{I}_2}{2r_2}$$ $\therefore \frac{{\mathrm{I}}_1}{{\mathrm{I}}_2}=\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}=\frac{2\mathrm{r}}{\mathrm{r}}$....(given $r_1=2r_2$ ) $\therefore \frac{{\mathrm{I}}_1}{{\mathrm{I}}_2}=2$...(ii) The resistance through the coil, $\mathrm{R}\propto l$ Here, $l=2\pi \mathrm{r}$ $\therefore \frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}=\frac{2\pi {\mathrm{r}}_1}{2\pi {\mathrm{r}}_2}=2$...(ii) $$\therefore \frac{{\mathrm{V}}_1}{{\mathrm{V}}_2}=\frac{{\mathrm{I}}_1{\mathrm{R}}_1}{{\mathrm{I}}_2{\mathrm{R}}_2}=2\times 2=4$$ [From (i) and (ii)]