Question

A silver wire (specific resistance $1.6\times {10}^{-8}\Omega m$) has a length of $4.9m$ and diameter $1mm$. The resistance of the wire is:

• A. $0.025\Omega$
• B. $0.1\Omega$
• C. $1\Omega$
• D. $2.5\Omega$

Answer 1

The correct option is B $0.1\Omega$

Diameter of the wire $d=1mm=1\times {10}^{-3}m$

Area of cross-section of wire $A=\frac{\pi }{4}(d{)}^2=\frac{\pi }{4}(1\times {10}^{-3}m{)}^2=7.85\times {10}^{-7}{m}^2$

Length $l=4.9m$

Specific resistance $\rho =1.6\times {10}^{-8}\Omega -m$

We know that

$R=\rho \frac{l}{A}$

$R=(1.6\times {10}^{-8})\left(\frac{4.9}{7.85\times {10}^{-7}}\right)$

$R=0.099\approx 0.1\Omega$