Question

Two wires of the same material and having lengths in the ratio of 2:3 are connected in series. The p.d.s across the wires are 4.2 V and 3.6 V respectively. Compare their radii.

• A. 1 : 7
• B. $2:\sqrt{7}$
• C. $\sqrt{2}:7$
• D. $\sqrt{2}:1$

Answer 1

The correct option is B $2:\sqrt{7}$

$\begin{array}{c}\text{Grven wires are in series that means current in both wires}\\ \text{is same let it be i.}\end{array}$

$\begin{array}{c}\text{Given lengths are in the ratio}2:3\text{and potential}\\ \text{difference across the wires are}4.2v\text{and}3.6V\text{.}\\ \text{Let the radii be}{r}_1,r_2\text{respectively.}\end{array}$

$V=iR\Rightarrow V=\frac{i\times \rho l}{A}$

$\begin{array}{c}\text{(Since wires are of Same}\\ \text{material)}\end{array}$

$4.2=\frac{P{\rho }^{}{l}_1}{\pi r_1^2}\to \left(i\right)$

$\text{3.}6=\frac{\text{i}\rho l_2}{\pi r_2^2}\to \left(ii\right)$

$\frac{\left(1\right)}{\left(2\right)}=\frac{4.2}{3.6}$$=\frac{7}{6}=\left(\frac{l_1}{l_2}\right)\times \frac{r_2^2}{r_1^2}$

$r_1:r_2=2:\sqrt{7}$