Q13 of 27 Page 1

The figure below shows three cylindrical copper conductors along with their face areas and lengths. Compare the resistance and the resistivity of the three conductors. Justify your answer.

The resistance of the three conductors in decreasing order of resistance is as follows:

Rb > Ra > Rc


Explanation:


1. Now in the given figure, the length and the area of the three conductors is varied.


2. We know the basic relationship between the resistance and the specific resistivity of the conductors is given as follows:


Resistance, Ra = (ρ × L) / A


Where,


ρ = Specific Resistivity of the conductor.


L = length of the conductor


A = Cross-Sectional Area of the conductor.




So resistance of second conductor = 9 R1




So resistance of the third conductor =


3. So, it can be proved that as cross-sectional area increases resistance decreases and as length increases resistance also increases.


4. So resistance of the three conductors in decreasing order of resistance is as follows:


Rb > Ra > Rc


5. Resistance is the obstruction to the flow of electrons. If the cross-sectional area of the conductor is large, there will less electron collision and hence there will be less resistance.


6. However, if the length increases the chances of electron collision is high, and hence resistance also increases.


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