Question

Resistance of a metal wire of length 0.5 m is 13 Ω at 20°C. If the diameter of the wire is 0.4 mm, resistivity of the metal at that temperature is
1 point
6.53x10*-8 ohm
6.53 x 10*-8 ohm m
6.53 x10*-6 ohm
6.53 x 10*-6 ohm m​

Answer 1

Answer:

6.53×10*-6 ohm- m

is the right ans.

Answer 2

Given:

Resistance of a metal wire of length 0.5 m is 13 Ω at 20°C. The diameter of the wire is 0.4 mm.

To find:

Resistivity at that temperature of that metal.

Calculation:

The general expression for resistance is:

$\boxed{ \sf{R = \rho \times ( \dfrac{l}{a} )}}$

Now , putting available values:

$= > \sf{13 = \rho \times \bigg \{\dfrac{0.5}{ (\frac{\pi {d}^{2} }{4}) } \bigg \}}$

$= > \sf{13 = \rho \times \bigg \{\dfrac{2}{ \pi {d}^{2} } \bigg \}}$

$= > \sf{13 = \rho \times \bigg \{\dfrac{2}{ \pi {(0.4 \times {10}^{ - 3}) }^{2} } \bigg \}}$

$= > \sf{13 = \rho \times \bigg \{\dfrac{2}{ \pi {(4 \times {10}^{ - 4}) }^{2} } \bigg \}}$

$= > \sf{13 = \rho \times \bigg \{\dfrac{2}{ \pi \times 16 \times {10}^{ - 8} } \bigg \}}$

$= > \sf{13 = \rho \times \bigg \{\dfrac{1}{ \pi \times 8 \times {10}^{ - 8} } \bigg \}}$

$= > \sf{ \rho = 13 \times 8\pi \times {10}^{ - 8} }$

$= > \sf{ \rho = 326.7\times {10}^{ - 8} }$

$= > \sf{ \rho = 3.267\times {10}^{ - 6} \: ohm \: m}$

So, final answer is:

$\boxed{\bf{ \rho = 3.267\times {10}^{ - 6} \: ohm \: m}}$