Question

Two wires of the same material having lengths in the ratio of 1 : 2 and diameters in the ratio 2 : 1 are connected with a cell of 6 volt and internal resistance $1\Omega$. The ratio of the potential difference across the two wires will be:

• A. $1:2$
• B. $2:1$
• C. $1:8$
• D. $8:1$

Answer 1

The correct option is C $1:8$

$L^{\prime }=2L$
$r^{\prime }=\frac{r}{2}⟹A^{\prime }=\frac{A}{4}$
We know,
R $=\frac{\rho \times L}{A}$
Hence,
$\frac{R^{\prime }}{R}=\frac{L^{\prime }}{L}\times \frac{A}{A^{\prime }}=\frac{2L}{L}\times \frac{A}{\frac{A}{4}}=8$
Hence,
$R^{\prime }=8R$
Assuming the resistors are connected in series,the current is same through both the resistors.
Using $I=\frac{V}{R};I=\frac{V^{\prime }}{R^{\prime }}$
We get,
$\frac{V}{V^{\prime }}=\frac{R}{R^{\prime }}=\frac{1}{8}$