An electronics technician evaluates how different physical modifications alter the electri… — Armed Services Vocational Aptitude Battery (ASVAB)

An electronics technician evaluates how different physical modifications alter the electrical resistance of solid wire conductors based on the fundamental relationship $R = \rho \frac{L}{A}$ . Match each conductor modification on the left with its exact resulting effect on electrical resistance on the right.

Doubling the total length ( $L$ ) of a uniform conductorDoubles the total resistance directly
Doubling the diameter ( $d$ ) of a cylindrical conductorDecreases total resistance to one-fourth ( $\frac{1}{4}$ ) of the initial value
Substituting a copper conductor with an identically sized nichrome conductorGreatly increases resistance due to the higher intrinsic material resistivity ( $\rho$ )
Substantially raising the operating temperature of a metallic conductorIncreases resistance due to increased electron collisions from thermal lattice vibration

Answer

Doubling conductor length doubles resistance; doubling diameter reduces resistance to one-fourth; replacing copper with nichrome increases resistance due to higher resistivity; increasing metal temperature increases resistance due to thermal lattice vibrations.

Each physical conductor property maps directly to the governing formula

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

and temperature coefficient behavior. Length is directly proportional (

2L \rightarrow 2R

), diameter has an inverse-square relationship (

2d \rightarrow 4A \rightarrow \frac{1}{4}R

), material change alters

\rho

, and thermal excitation increases atomic collisions in metals.

Step-by-Step Solution

Analyze the effect of length change using

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

Since

R \propto L

, multiplying length by

2

multiplies resistance by

2

Electrons must traverse twice as much resistive medium, doubling opposition to flow.

Analyze the effect of diameter change using cross-sectional area

A = \frac{\pi d^2}{4}

Doubling

d

yields

(2d)^2 = 4A

. Since

R \propto \frac{1}{A}

, resistance becomes

\frac{R}{4}

Resistance varies inversely with the square of the conductor diameter.

Analyze material substitution from copper to nichrome

Nichrome has a higher resistivity (

\rho

) than copper.

Resistivity is an intrinsic material property that directly scales total resistance.

Analyze thermal effects on metallic conductors

Resistance increases with temperature in standard metals.

Thermal energy increases lattice atom vibrations, creating more frequent collisions with moving valence electrons.

Key Concept

Physical factors determining conductor resistance: length, cross-sectional area, resistivity, and temperature

Estimated Time:1m 15s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic