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Zorluk: KolayResistance and Resistivity

A piece of copper hookup wire with a length of 15 m15\text{ m} has an electrical resistance of 0.6 Ω0.6\ \Omega. If the wire is replaced with a 45 m45\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 (Ω\Omega)?

Cevap: 1.8 \Omega

Cevap

1.8 \Omega
According to the fundamental resistance relationship R=ρLAR = \rho \frac{L}{A}, resistance is directly proportional to the length LL of the conductor when resistivity ρ\rho and cross-sectional area AA remain unchanged. Tripling the wire length from 15 m15\text{ m} to 45 m45\text{ m} multiplies the resistance by a factor of 3, resulting in 0.6 Ω×3=1.8 Ω0.6\ \Omega \times 3 = 1.8\ \Omega.

Adım Adım Çözüm

1
Calculate the proportional change in conductor length.
The new length is 3 times the original length (45 m÷15 m=345\text{ m} \div 15\text{ m} = 3).
Identifying the scaling factor allows direct application of the resistance formula.
2
Apply the direct proportionality between conductor length and electrical resistance (R∝LR \propto L).
Rnew=Rold×3=0.6 Ω×3=1.8 ΩR_{\text{new}} = R_{\text{old}} \times 3 = 0.6\ \Omega \times 3 = 1.8\ \Omega.
Since material resistivity (ρ\rho) and cross-sectional area (AA) are held constant, tripling the length triples the total resistance.

Anahtar Kavram

The electrical resistance of a uniform conductor is directly proportional to its length (R=ρLAR = \rho \frac{L}{A}).
Tahmini Süre:45s
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Resistance and Resistivity

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