A piece of copper hookup wire with a length of 15\text{ m} has an electrical resistance of… — Armed Services Vocational Aptitude Battery (ASVAB)

A piece of copper hookup wire with a length of $15\text{ m}$ has an electrical resistance of $0.6\ \Omega$ . If the wire is replaced with a $45\text{ m}$ piece of the exact same wire type and gauge at the same temperature, what is the resistance of the new wire in ohms ( $\Omega$ )?

Answer: 1.8 \Omega

Answer

1.8 \Omega

According to the fundamental resistance relationship

R = \rho \frac{L}{A}

, resistance is directly proportional to the length

L

of the conductor when resistivity

\rho

and cross-sectional area

A

remain unchanged. Tripling the wire length from

15\text{ m}

45\text{ m}

multiplies the resistance by a factor of 3, resulting in

0.6\ \Omega \times 3 = 1.8\ \Omega

Step-by-Step Solution

Calculate the proportional change in conductor length.

The new length is 3 times the original length (

45\text{ m} \div 15\text{ m} = 3

Identifying the scaling factor allows direct application of the resistance formula.

Apply the direct proportionality between conductor length and electrical resistance (

R \propto L

R_{\text{new}} = R_{\text{old}} \times 3 = 0.6\ \Omega \times 3 = 1.8\ \Omega

Since material resistivity (

\rho

) and cross-sectional area (

A

) are held constant, tripling the length triples the total resistance.

Key Concept

The electrical resistance of a uniform conductor is directly proportional to its length (

R = \rho \frac{L}{A}

Estimated Time:45s

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