Question

Nichrome and copper wire of same length and same radius are connected in series. Current I is passing through them. Which wire gets heated up more? Justify your answer.

Answer 1

Hint: We should know that; nichrome is an alloy and copper is a pure metal. And during an alloy formation the change in its resistivity takes place and due to which the resistivity of alloy increases as compared to the pure metal.

Complete step by step solution:
We have been given two materials, nichrome and copper, both having the same length and radius and have been connected in series so that same current flows through them.
Since, nichrome is an alloy and in a metallic alloy, in which we mix higher conductivity material to other metals and which ultimately increases the resistivity of the parent metal or the resistivity of the alloy increases. It happens because of the increase in scattering centers in the alloys in respect to metals. As resistivity is the inverse of conductivity which is in general a tensor quantity of rank two which connects two vector quantities viz. electric field and current density and it doesn’t follow any simple additive role for resistivity.
Copper is a metal and thus has resistivity lower than that of an alloy and so lower than nichrome.
Since, resistance is directly proportional to resistivity and so the copper will have less resistance than nichrome. Now, we can use the formula for heat generated which is given by
$H=I^2 Rt$, where I is the current, R is the resistance and t is the time. And since resistance of nichrome is greater than that of copper.
Hence, heat generated in the nichrome will be more than that of the copper.

Note: Since, we have been given that the length and cross section is same for both materials given, so we may get confused and consider the heat generated in both same and so we should know that the resistance further depends on resistivity and which is different for different materials.