two wires A and B of …
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two wires A and B of which length are in the ratio 1: 2 and the area of cross section area in the ratio 2: 1 and of same is resistivity are connected in parallel with the same source of emf. find the ratio of drift velocity in the given two wires.
Posted by Sarbjit Singh 6 years, 2 months ago
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Sia ? 6 years, 2 months ago
As we know, {tex}\Delta{/tex}L = {tex}\frac{FL}{AY}{/tex}, {tex}\frac{L_A}{L_B}{/tex} = {tex}\frac{1}{2}{/tex} and {tex}\frac{r_A}{r_B}{/tex} = {tex}\frac{1}{2}{/tex}
[{tex}\therefore{/tex} the wires {tex}A\ and\ B{/tex} are pulled by the same force and they are made up of same material, hence, {tex}F_A = F_B = F, = Y_A = Y_B = Y{/tex}]
{tex}\frac{\Delta L_A}{\Delta L_B}{/tex} = {tex}\frac{L_{A}}{\pi r_{A}^{2}} \times \frac{\pi r_{B}^{2}}{L_{B}}{/tex}
{tex}\frac{\Delta L_{A}}{\Delta L_{B}}{/tex} = {tex}\frac{L_{A}}{L_{B}} \times\left(\frac{r_{B}}{r_{A}}\right)^{2}{/tex}
{tex}\frac{\Delta L_{A}}{\Delta L_{B}}{/tex} = {tex}\frac{1}{2} \times\left(\frac{1}{2}\right)^2{/tex}= {tex}\frac{1}{2}{/tex}
{tex}\frac{\Delta L_{A}}{\Delta L_{B}}{/tex}= {tex}\frac{1}{8}{/tex}
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