Question

A copper wire and a Nichrome wire were found to have the same resistance.

1. Will the two wires have the same resistivity also? Justify your answer.
2. Give an example of a pure metal having high resistivity.
3. What is the unit of resistivity?

Answer 1

The given question can easily be answered if we know about resistance of a body and the criteria on which the resistance depends. Also, we need to know the formula of resistance based on these criteria which is $R = \rho \dfrac{l}{A}$. We can compare the question with the values of resistance and write the correct answer of the given question.

Complete answer:
First of all let us write the equation of resistance and find out the parameters on which the resistance depends.
So, we have $R = \rho \dfrac{l}{A}$.
R = resistance of the wire.
l = length of the wire.
A = cross-sectional area of the wire
$\rho$= resistivity of the wire
Clearly, we can notice that the resistance of a body depends on the length, area and the resistivity of the body. Also, different materials have different values of resistivity.
Now, we can answer the sub parts of the question.
1. Even though the wires of copper and Nichrome have the same resistance and length but their resistivity will be different. So, wires of different materials cannot have the same resistance.
2. Tungsten, Nichrome are the metals with very high resistivity.
3. The unit of resistivity is ohm-meter or $\Omega m$.

Note: We should not get confused with the value of resistance using Ohm’s law relation. According to Ohm/s law voltage is directly proportional to the current in a body. Mathematically, we write it as, $V = IR$. Here, the resistance is the ratio of voltage and current but it does not change with the current or voltage supply.