A conducting wire is quadrupled in length and tripled in diameter.

Does its resistance increase, decrease, or stay the same?

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