Answer:
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Answer:
Its resistance decreases
Explanation:
The resistance of a wire is directly proportional to the length of the wire and inversely proportional to the cross sectional area of the wire.
Mathematically,
R1 =¶L1/A1... (1)
R1= ¶L1/{Πd²/4}
R1= 4¶L1/Πd²
where;
¶ is the constant of proportionality which is the resistivity of the material
L is the length of the wire
A is the cross sectional area
A1 = Πd²/4
If the length is quadrupled and its diameter tripled
The new length L2 will be 4L1
New area A2 = Π(3d)²/4 = 9Πd²/4
The resistance will become
R2 = ¶(4L1)/{9Πd²/4}
R2 = 4¶L1×4/9Πd²
R2 = 16¶L1/9Πd²... (2)
R2/R1 = 16¶L1/9Πd²÷4¶L1/Πd²
R2/R1 = 16¶L1/9Πd²×Πd²/4¶L1
R2/R1 = 16/9×1/4
R2/R1 = 16/36
R2/R1 = 4/9
R2 = 4/9R1
This shows that the resistance of the wire decreases
