A wire 50 cm long  1 mm2 in cross–section carries a current of 4A when connected to a 2V battery. The resistivity of the wire is

# A wire $50\text{\hspace{0.17em}}\mathrm{cm}$ long  $1\text{\hspace{0.17em}}{\mathrm{mm}}^{2}$ in cross–section carries a current of 4A when connected to a 2V battery. The resistivity of the wire is

1. A

$2×{10}^{-7}\text{\hspace{0.17em}}\mathrm{\Omega m}$

2. B

$5×{10}^{-7}\text{\hspace{0.17em}}\Omega m$

3. C

$4×{10}^{-6}\text{\hspace{0.17em}}\mathrm{\Omega m}$

4. D

$1×{10}^{-6}\text{\hspace{0.17em}}\mathrm{\Omega m}$

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### Solution:

Length$l=50\mathrm{cm}$  Cross-sectional area  $A=1{\mathrm{mm}}^{2}=1×{10}^{-6}\mathrm{m}$
Current $\mathrm{i}=4\mathrm{A}$ Potential difference $\mathrm{V}=2\mathrm{V}$
Resistance  $\mathrm{R}=\frac{\mathrm{V}}{\mathrm{I}}=\frac{2}{4}=0.5\mathrm{\Omega }⇒\mathrm{\rho }=\frac{\mathrm{RA}}{\mathrm{\ell }}=\frac{0.5×{10}^{-6}}{50×{10}^{-2}}\therefore \mathrm{\rho }={10}^{-6}\mathrm{\Omega m}$

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