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  • A uniform metallic wire carries a current 2A, when 3.4 V battery is connected across it. The mass of uniform metallic wires is 8.92 <img alt="\times 10^{-3} \mathrm{~kg}" src="https://entrance

A uniform metallic wire carries a current 2A, when 3.4 V battery is connected across it. The mass of uniform metallic wires is 8.92 \times 10^{-3} \mathrm{~kg} density  8.92\times 10^3 \mathrm{~kg} / \mathrm{m}^3and resistivity is 17 \times 10^{-8} \Omega-\mathrm{m}The length of wire is:

Option: 1

l = 10 m


Option: 2

l = 100 m


Option: 3

l = 100 m


Option: 4

l = 6.8 m


Answers (1)

best_answer


Given, i = 2A
v = 3.4 v
v = iR
\mathrm{R}=\frac{\mathrm{v}}{\mathrm{i}}=\frac{3.4}{2}=1.7 \Omega
\begin{aligned} & \text { volume }=\frac{\text { mass }}{\text { Density }}=\frac{8.92 \times 10^{-3}}{8.92 \times 10^3} \mathrm{~m}^3=10^{-6} \mathrm{~m}^3 \\ & \Rightarrow \mathrm{A} \ell=10^{-6} \mathrm{~m}^3 \quad \text { (i) } \\ & \mathrm{R}=\frac{\rho \ell}{\mathrm{A}} \\ & \Rightarrow \frac{\rho}{\mathrm{R}}=\frac{A}{\ell} \end{aligned}
\begin{aligned} & \frac{1.7 \times 10^{-8}}{1.7}=\frac{A}{\ell} \\ & \frac{\mathrm{A}}{\ell}=10^{-8} \\ & \frac{\mathrm{eq}(\mathrm{i})}{\mathrm{eq}(\mathrm{ii})} \\ & \ell^2=10^2 \\ & \ell=10 \mathrm{~m} \end{aligned}

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rishi.raj

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