Which of the following statements are true with regard to resistance?

Question

Examoogle · Accepted Answer

Resistance is directly proportional to the length of the wire

Explanation: Resistance ($R$) of a conductor is fundamentally dependent on its material, geometry, and temperature. For a uniform conductor of length $l$ and cross-sectional area $A$, the resistance is directly proportional to its length and inversely proportional to its area of cross-section.

Working Principle: As the length of a conductor increases, the number of electron collisions with atoms increases, which increases the opposition to current flow (resistance). Conversely, an increase in cross-sectional area provides more paths for electrons, effectively reducing the resistance in a manner analogous to adding resistors in parallel.

Key Formulas: $R = \rho \frac{l}{A}$ — Where $R$ is resistance, $\rho$ is resistivity, $l$ is length, and $A$ is area.; $\rho = R \frac{A}{l}$ — Calculating resistivity in $\Omega \cdot m$.

Key Points: Resistance is directly proportional to length ($R \propto l$).; Resistance is inversely proportional to cross-sectional area ($R \propto \frac{1}{A}$).; Resistivity ($\rho$) is a property of the material itself and is independent of dimensions.; Higher temperature typically increases the resistance of metallic conductors.

Advantages: Uniform calculation for wire sizing in electrical installations.; Predictable behavior for circuit design and voltage drop compensation.

Disadvantages: Real-world conductors vary in resistivity due to temperature fluctuations.; Surface effects (skin effect) at high frequencies make simple DC formulas inaccurate.

Applications: Transmission line design; Resistor manufacturing; Electrical wiring in buildings

Additional Info: Option B is incorrect because resistance is inversely proportional to cross-sectional area, not directly.. Option C is incorrect because resistance increases with length.. Option D is incorrect because resistance is directly proportional to resistivity.

Answer: A is correct — Resistance is directly proportional to the length of the wire, meaning $R \propto l$.

Exam Tip: Remember the mnemonic 'L/A' to recall that resistance increases with length and decreases with cross-sectional area.

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