Question

The resistance of a wire of length 300m and cross-sectional area $1.0m{{m}^{2}}$ made of material of resistivity $1.0\times {{10}^{-7}}\Omega m$ is:
$\begin{align}
  & (A)2\Omega \\
 & (B)3\Omega \\
 & (C)20\Omega \\
 & (D)30\Omega \\
\end{align}$

Answer 1

Hint: We have to calculate the total resistance of the wire for the given values of different parameters. We shall use the formula of resistance, which is, the resistance of a wire can be written as the product of its length and resistivity upon its cross-sectional area. Also, before putting all the values in the mentioned formula, we will make sure they all have the same units.

Complete answer:
Let the length of the wire be given by $L$.
Then it has been given to us in the problem that the value of $L$ is 300 meters.
Now, let the area of cross-section of the wire be A. Then, it has been given to us that:
$\Rightarrow A=1.0m{{m}^{2}}$
We will convert this Area of cross-section into meter squared so that all the units remain consistent with each other upon calculation:
Since,
$\Rightarrow 1mm={{10}^{-3}}m$
Therefore,
$\Rightarrow 1m{{m}^{2}}={{10}^{-6}}{{m}^{2}}$
And, let the resistivity of the given wire be denoted by $\rho $.
Also, the value of resistivity has been given to us in the problem as:
$\Rightarrow \rho =1.0\times {{10}^{-7}}\Omega m$
Now, we can calculate the resistance of the metal wire with the help of the given formula:
$\Rightarrow R=\dfrac{\rho L}{A}$
Putting the values of all the terms in Right Hand Side of the equation, we get:
$\begin{align}
  & \Rightarrow R=\dfrac{1.0\times {{10}^{-7}}\times 300}{{{10}^{-6}}} \\
 & \Rightarrow R=300\times {{10}^{-1}} \\
 & \Rightarrow R=30\Omega \\
\end{align}$
Hence, the resistance of the wire comes out to be $30\Omega $ .

Hence, option (D) is the correct option.

Note:
These are some basic formulas from one of the most important chapters of Physics, Current Electricity. So, one should very well be aware of these basic formulas. Also, one should always keep check of their calculations at every step of solution or else one small error might end up giving a wrong solution to our problem.