Question

A copper wire of cross-sectional area $3.4m{{m}^{2}}$ and length of the wire $400m$, specific resistivity of copper is $1.7\times {{10}^{-8}}\Omega m$. The resistance of the wire is
(A). $20\Omega $
(B). $200\Omega $
(C). $2\Omega $
(D). $2k\Omega $

Answer 1

Hint: An element opposes the flow of current through it f=due to its resistance. Resistance in circuit along with the potential difference at the ends of circuit determines the current flowing through the circuit. The resistance of a material depends on the type of material as well as its dimensions.

Formula used:
$R=\dfrac{\rho l}{A}$

Complete step-by-step solution:
The property of a material by virtue of which it opposes the flow of current through it is called its resistance. Its SI unit is $\Omega $.

According to Ohm’s law, resistance is given by
$R=\dfrac{V}{I}$
Here, $R$ is the resistance
$V$ is the potential difference applied at the ends
$I$ is current flowing between the ends

Resistance depends on the type of material as well as the dimensions. Its is also given by-
$R=\dfrac{\rho l}{A}$ - (1)
Here, $\rho $ is the resistivity of the material
$l$ is the length
$A$ is the area of cross section

Given, a wire has specific resistivity $1.7\times {{10}^{-8}}\Omega m$, its length is $400m$ and area is $3.4m{{m}^{2}}$. Substituting given values in eq (1), we get,
$\begin{align}
  & R=\dfrac{1.7\times {{10}^{-8}}\times 400}{3.4\times {{10}^{-6}}} \\
 & \Rightarrow R=200\times {{10}^{-2}}\Omega \\
 & \therefore R=2\Omega \\
\end{align}$
The resistance of the wire is $2\Omega $.

Therefore, the resistance of the wire is $2\Omega $. Hence, the correct option is (C).

Note:
The specific resistance or resistivity is defined as the resistance of an element of unit length and unit area of cross section. It is a constant quantity and is different for different materials. It depends on temperature. Copper is a metal, hence it is a very low resistance. The resistance in metals is lowest, in semiconductors, the resistance is more than conductors while in insulators, the resistance is the highest.