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Question: A nichrome wire 1m long and \[1m{{m}^{2}}\] in a cross-sectional area draws 4 ampere at 2 volt. The ...

A nichrome wire 1m long and 1mm21m{{m}^{2}} in a cross-sectional area draws 4 ampere at 2 volt. The resistivity of nichrome is
A. 1×10−7Ωm1\times {{10}^{-7}}\Omega m
B. 2×10−7Ωm2\times {{10}^{-7}}\Omega m
C. 4×10−7Ωm4\times {{10}^{-7}}\Omega m
D. 5×10−7Ωm5\times {{10}^{-7}}\Omega m

Explanation

Solution

Hint: In the question, resistance of the wire is not given. It has to be calculated from the voltage and current. This resistance can be used to find the resistivity of that wire by using the following equation. ρ=RAl\rho =\dfrac{RA}{l}

Complete step-by-step answer:
Resistance of the wire can be written as,
R=VIR=\dfrac{V}{I}, where VV is the voltage and II is the current.
Therefore, the resistance will be,
R=24=0.5AR=\dfrac{2}{4}=0.5A
The given wire has one metre length and 1mm21m{{m}^{2}} cross-sectional area.
We have to convert this area into SI units. Therefore,
1mm2=10−6m21m{{m}^{2}}={{10}^{-6}}{{m}^{2}}
Length of the wire is already in the SI unit. So, we don’t have to change that.
Thus, resistivity of the wire can be written as,
ρ=RAl\rho =\dfrac{RA}{l}, where A is the area of cross-section and l is the length of the wire.
We can assign values into the equation.
ρ=0.5×10−61\rho =\dfrac{0.5\times {{10}^{-6}}}{1}
So, the resistivity will be,
ρ=5×10−7Ωm\rho =5\times {{10}^{-7}}\Omega m
Hence the correct option is D.

Additional information:
Resistivity is a property of a material and that can tell about how strongly a material opposes the flow of electrical current. Resistance will increase according to the resistivity and length increment. While the area shows inverse relationship with resistance. Temperature is also affecting the resistance.
We can discuss some materials that have been used for circular wires in various applications.
Copper; Widely used material due to its high malleable and ductile properties and it is commonly available.
Aluminium; Its thermal characteristics made them uncommon for general wiring purposes.
Silver and Gold; They can be used for the wiring. But the cost will be very high.
Tungsten; Due to its high resistivity, durability and hardness, they are used in some other applications.

Note: To find the resistivity you have to calculate the resistance also. Don’t forget to convert the cross-sectional area into the SI unit. Since all other quantities are in SI units.