Concept explainers
To explain:
Whether two wires, one of copper and other of aluminum can have the same resistance, if their lengths are same.
Answer to Problem 4Q
Solution:
Yes, they can have the same resistance if the two wires have different cross-sectional areas.
Explanation of Solution
Formula used: The resistance ( R ) of a resistor is related to the resistivity of its material ( ρ ), it’s length ( l ) and the cross-sectional area ( A ) as,
Where, D is the diameter of the resistor.
The resistance of a resistor depends on the resistivity of its material ( ρ ), it’s length ( l ) and the cross-sectional area ( A ) as,
So, if we take up two wires of different materials like one of copper and other aluminum, their resistivity would be different. Now, if their length is also equal and we want their resistance to be the same, then it will be possible only with different cross-sectional areas, i.e., their diameters must be different.
or,
or,
Conclusion
It is quite possible to have the same resistance in the copper and aluminum wires of the same length if the ratio of their diameters is equal to the square-root of their resistivity.
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