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Physics · 2024 · 2 marks
CBSE 2024 · Region 4 · Set 2 · Q20
Two wires A and B of different metals have their lengths in ratio 1: 2 and their radii in ratio 2:1 respectively. I-V graphs for them is shown in the…
Two wires A and B of different metals have their lengths in ratio $\displaystyle 1: 2$ and their radii in ratio $\displaystyle 2$:$\displaystyle 1$ respectively. I-V graphs for them is shown in the figure. Find the ratio of their
(i)
Resistances $\displaystyle \left(R_{\mathrm{A}} / R_{\mathrm{B}}\right)$ and
(ii)
Resistivities $\displaystyle \left(\sigma_{\mathrm{A}} / \sigma_{\mathrm{B}}\right)$
Marking-scheme solution
(i)
Slope of I-V graph $\displaystyle =\left(\frac{\Delta I}{\Delta V}\right)=\frac{I}{R}$
$\displaystyle \frac{R_{A}}{R_{B}}=\frac{\text { Slope of } B}{\text { Slope of } A}$
$\displaystyle =\frac{\tan 45^{\circ}}{\tan 30^{\circ}}$
$\displaystyle \frac{R_{A}}{R_{B}}=\sqrt{3}$
(ii)
$\displaystyle \frac{\sigma_{A}}{\sigma_{B}}=\frac{\dfrac{R_{A} A_{A}}{l_{A}}}{\dfrac{R_{B} A_{B}}{l_{B}}}$
$\displaystyle =\frac{R_{A}}{R_{B}} \cdot \frac{A_{A}}{A_{B}} \cdot \frac{l_{B}}{l_{A}}$
$\displaystyle =\sqrt{3} \times \frac{4}{1} \times \frac{2}{1}$
$\displaystyle =8 \sqrt{3}$
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