Which combination of factors would result in the lowest resistance for a conductor?

Question

Examoogle · Accepted Answer

The correct answer is Option B: Short length and large cross-sectional area. Resistance ($R$) of a conductor is directly proportional to its length ($l$) and inversely proportional to its cross-sectional area ($A$). To achieve the lowest resistance, one needs a conductor with the shortest possible length and the largest possible cross-sectional area.

Step-by-Step Solution & Concepts:
Resistance ($R$) of a conductor is directly proportional to its length ($l$) and inversely proportional to its cross-sectional area ($A$). To achieve the lowest resistance, one needs a conductor with the shortest possible length and the largest possible cross-sectional area.

Working Principle: According to the law of resistance, $R = \rho \frac{l}{A}$, where $\rho$ is the resistivity of the material. A shorter length ($l$) reduces the number of collisions electrons encounter while traveling through the conductor, and a larger cross-sectional area ($A$) provides a wider 'path' for charge carriers to flow, effectively reducing obstruction.

Key Formulas: $R = \rho \frac{l}{A}$ — Resistance formula where $\rho$ is resistivity, $l$ is length, and $A$ is cross-sectional area.; $I = \frac{V}{R}$ — Ohm's Law relating current, voltage, and resistance.

Key Points: Resistance is directly proportional to length: $R \propto l$.; Resistance is inversely proportional to cross-sectional area: $R \propto \frac{1}{A}$.; Thick wires have lower resistance than thin wires of the same material.; Short wires have lower resistance than long wires of the same material.

Advantages: Lower resistance leads to reduced heat dissipation ($I^2R$ losses).; Efficient power transmission over thick conductors.

Disadvantages: Large cross-sectional area wires are heavier and more expensive (use more copper/aluminum).

Applications: High-tension power transmission lines.; Electrical grounding systems to ensure low-impedance paths for fault currents.

Additional Info: Resistivity ($\rho$) is an intrinsic property of the material and does not change with geometry.. Option A results in moderate resistance, Option C in very high resistance, and Option D in moderate resistance.

Answer: B is correct — Resistance is minimized when the length is short and the cross-sectional area is large, as per the formula $R = \rho \frac{l}{A}$.

Exam Tip: Always remember the 'pipe analogy' for electricity: Voltage is pressure, Current is flow rate, and Resistance is pipe diameter/length/friction.

Examoogle · Answer

Option A: Short length and small cross-sectional area

Examoogle · Answer

Option C: Long length and small cross-sectional area

Examoogle · Answer

Option D: Long length and large cross-sectional area

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