Copper wire #1 has a length L and a radius b. Copper wire #2 has a length 2L and

Question

Copper wire #1 has a length L and a radius b. Copper wire #2 has a length 2L and a radius 2b. Which statement is true?

Answer

The total resistance of wire #1 is equal to that of wire #2.

The total resistance of wire #1 is twice as high as that of wire #2.

The total resistance of wire #1 is four times higher than that of wire #2.

The total resistance of wire #1 is half that of wire #2.

Explanation / Answer

Resistance R = ?* L / A For wire #1, resistivity = ? Length L = L area of crosssection A = pb2 => R1 = ?* L / pb2 For wire #2 resistivity = ? length = 2L area of crosssection = p *(2b)2 = 4pb2 => R2 = ?* 2L / 4pb2 Dividing R1 byR2 R1 /R2 = (? * L /pb2) / (? * 2L / 4pb2) = 2 R1 = 2* R2 The total resistance of wire #1 is twice ashigh as that of wire #2.

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