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JEE MAINS 2023
25.01.23
Question
A uniform metallic wire carries a current 2 A. when 3.4 V battery is connected across it. The mass of uniform metallic wire is 8.92 × 10–3 kg. density is 8.92 × 103 kg/m3 and resistivity is 1.7 × 10–8 -m. The length of wire is
Select the correct option:
A
l = 6.8 m
B
l = 10 m
C
l = 5 m
D
l = 100 m
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Sol. $$ \begin{aligned} & I=2 \mathrm{~A} \\ & \Delta \mathrm{~V}=3.4 \mathrm{~V} \\ & \text { Using Ohm's Law } \end{aligned} $$ $$ \begin{aligned} & R=\frac{3.4}{2}=1.7 \Omega \\ & 1.7=\frac{\rho L}{A} \\ & L=\frac{1.7(A)}{\rho} \end{aligned} $$ $\mathrm{M}=$ (density volume) $$ \begin{aligned} \text { Volume } & =\frac{8.92 \times 10^{-3}}{8.92 \times 10^3}=10^{-6} \\ & L^2=\frac{1.7}{\rho}\left(10^{-6}\right)=\frac{1.7}{1.7} \times 10^2 \\ L & =10 \mathrm{~m} \end{aligned} $$
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