Two wires of the same material have length  6 cm and 10 cm   and radii 0.5 mm and 1.5 mm respectively. They are connected in series across a battery of  16 V.  The potential difference. across the shorter wire is

# Two wires of the same material have length  6 cm and 10 cm   and radii $0.5\text{\hspace{0.17em}}\mathrm{mm}$ and $1.5\text{\hspace{0.17em}}\mathrm{mm}$ respectively. They are connected in series across a battery of  $16\text{\hspace{0.17em}}\mathrm{V}$.  The potential difference. across the shorter wire is

1. A

$5\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{V}$

2. B

$\text{13.5\hspace{0.17em}\hspace{0.17em}V}$

3. C

$27\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{V}$

4. D

10 V

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### Solution:

Length ${l}_{1}=6\mathrm{cm}$ Length ${l}_{2}=10\mathrm{cm}$ Radius ${r}_{1}=0.5\mathrm{mm}$ Radius ${r}_{2}=1.5\mathrm{mm}$
$\mathrm{V}=\mathrm{iR}⇒\mathrm{i}\frac{\mathrm{\rho \ell }}{\mathrm{A}}⇒\frac{{\mathrm{V}}_{1}}{{\mathrm{V}}_{2}}=\frac{{\mathrm{\ell }}_{1}}{{\mathrm{\ell }}_{2}}×{\left[\frac{{\mathrm{r}}_{2}}{{\mathrm{r}}_{1}}\right]}^{2}⇒\frac{27}{5}$

${\mathrm{V}}_{1}+{\mathrm{V}}_{2}=16;{\mathrm{V}}_{2}=\frac{5{\mathrm{V}}_{1}}{27}$

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