$\mathrm{C} \propto \mathrm{N} \cdot \mathrm{A}$

Here $\quad \frac{\mathrm{N}_{\mathrm{A}}}{\mathrm{N}_{\mathrm{B}}}=\frac{1}{2}$

If $\mathrm{r}_{\mathrm{A}}$ and $\mathrm{r}_{\mathrm{B}}$ be the radii of the circular loops $\mathrm{A}$ and $\mathrm{B}$ respectively, then the length $\ell$ of both the wires,

${\ell=2 \pi \mathrm{r}_{\mathrm{A}}=2 \times 2 \pi \mathrm{r}_{\mathrm{B}}}$

${\mathrm{r}_{\mathrm{A}}=2 \mathrm{r}_{\mathrm{B}}}$

Their cross-sectional areas $\mathrm{A}_{\mathrm{A}}$ and $\mathrm{A}_{\mathrm{B}}$ are in the ratio

$\frac{\mathrm{A}_{\mathrm{A}}}{\mathrm{A}_{\mathrm{B}}}=\frac{\pi \mathrm{r}_{\mathrm{A}}^{2}}{\pi \mathrm{r}_{\mathrm{B}}^{2}}=4$

Now, the ratio of couples on the two coils is

${\frac{C_{A}}{C_{B}}=\frac{N_{A}}{N_{B}} \frac{A_{A}}{A_{B}}=\frac{1}{2} \times 4=2} $

${C_{A}=2 C_{B}}$