An avionics technician is evaluating how specific physical modifications and environmental… — Armed Services Vocational Aptitude Battery (ASVAB)

An avionics technician is evaluating how specific physical modifications and environmental conditions affect the electrical resistance of solid cylindrical conductors. Match each physical change on the left with its corresponding effect on electrical resistance on the right.

Uniformly stretching a wire to double its original length ( $2L$ ) while maintaining constant total volumeResistance increases by a factor of 4 ( $4R$ ) because the cross-sectional area is simultaneously halved
Doubling the cross-sectional diameter ( $2d$ ) of a wire while keeping its length and material unchangedResistance decreases to one-fourth of its initial value ( $\frac{1}{4}R$ ) because area scales with the square of diameter
Significantly increasing the operating temperature of a pure metallic conductorResistance increases because intensified thermal lattice vibrations increase the frequency of electron collisions
Replacing a conductor with one made of an intrinsically lower-resistivity material of identical dimensionsResistance decreases because the smaller resistivity value ( $\rho$ ) reduces resistance for the same geometric dimensions

Answer

Uniformly stretching a wire to double length at constant volume pairs with resistance quadrupling (

4R

); doubling wire diameter pairs with resistance decreasing to one-fourth (

\frac{1}{4}R

); heating a metallic conductor pairs with resistance increasing due to thermal lattice vibrations; and substituting a lower-resistivity material pairs with resistance decreasing proportionally.

Each physical modification maps directly to the governing formula

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

and thermal properties of conductors: stretching at constant volume doubles length while halving area (

2 / 0.5 = 4

); doubling diameter quadruples area reducing resistance to one-fourth; increasing temperature increases electron scattering in metals; and lower intrinsic material resistivity directly lowers resistance for identical dimensions.

Step-by-Step Solution

Analyze the volume-conserving elongation of a wire

Stretching to length

2L

at constant volume

V = A \cdot L

forces the cross-sectional area to become

A/2

, producing resistance

R' = \rho \frac{2L}{A/2} = 4R

Volume conservation requires that axial stretching produces a proportional lateral contraction.

Determine the effect of doubling wire diameter at fixed length

Cross-sectional area scales with diameter squared (

A \propto d^2

), so doubling diameter increases area by a factor of 4, reducing resistance to

R' = \frac{1}{4}R

Resistance is inversely proportional to cross-sectional area.

Evaluate the temperature dependence of resistance in metals

Elevated temperature increases lattice ion vibrations, which impedes electron drift and increases resistance.

Pure metallic conductors have a positive temperature coefficient of resistance.

Examine the direct role of material resistivity for identical geometry

From

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

, decreasing material resistivity

\rho

directly decreases resistance

R

Resistivity is the intrinsic property defining resistance per unit length and cross-sectional area.

Key Concept

Physical and material determinants of electrical resistance governed by

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

and temperature effects.

Estimated Time:1m 15s

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