Question

A cuboidal wire of length $0.07m$, has a square cross section of side $0.05m$ and resistivity of $0.0198\Omega$$m$. Find the resistance and the conductance of the wire.

• A. $R=0.454\Omega$ , $G=1.605\Omega {}^{-1}$
• B. $R=0.564\Omega$ , $G=1.805\Omega {}^{-1}$
• C. $R=0.554\Omega$ , $G=1.805\Omega {}^{-1}$
• D. $R=0.654\Omega$ , $G=1.856\Omega {}^{-1}$

Answer 1

The correct option is C $R=0.554\Omega$ , $G=1.805\Omega {}^{-1}$

Given:
Length, $l=0.07m$
Side, $a=0.05m$
Resistivity, $\rho =0.0198\Omega$$m$

We know,
Resistance, $R=\left(\frac{\rho l}{A}\right)$

$R=\left(\frac{0.0198\times 0.07}{0.05\times 0.05}\right)$

$⟹R=\frac{0.001386}{0.0025}$

$⟹R=0.554\Omega$

Conductance, $G=\frac{1}{R}$
$⟹G=\frac{1}{0.5544}$

$⟹G=1.804\Omega {}^{-1}$