For a fixed supply voltage the current flowing through a conductor will decrease when

Question

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length of the conductor is increased

Explanation: According to Ohm's Law ($I = \frac{V}{R}$), for a constant voltage $V$, current $I$ is inversely proportional to resistance $R$. The resistance of a conductor is determined by its physical dimensions and material property, defined as $R = \rho \frac{l}{A}$.

Working Principle: The resistance $R$ of a conductor increases linearly with length $l$ due to the increase in collisions of charge carriers as they traverse a longer path. Since $I = \frac{V}{R}$, an increase in $l$ leads to an increase in $R$, which consequently forces a decrease in current $I$ for a fixed supply voltage.

Key Formulas: $R = \rho \frac{l}{A}$ — formula for resistance based on geometry and resistivity; $I = \frac{V}{R}$ — 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: $R \propto \frac{1}{A}$; Increasing the length $l$ increases the resistance $R$ for a given conductor material and area; Higher resistance limits the flow of current in a DC circuit given a fixed voltage

Advantages: Predictable circuit behavior; Mathematical consistency with Ohm's Law

Disadvantages: Power loss in long conductors due to increased resistance; Voltage drop issues over long transmission distances

Applications: Design of resistors; Power transmission line engineering; Electronic circuit cabling

Additional Info: The constant $\rho$ (rho) represents the resistivity of the material in $\Omega \cdot m$.. Option A is incorrect because increasing area decreases resistance, which increases current.. Option C is incorrect because reducing length decreases resistance, which increases current.. Option D is incorrect because both increasing area and decreasing length work together to significantly reduce resistance, thus increasing current.

Answer: B is correct — Increasing the length of a conductor increases its resistance, which, according to Ohm's Law, results in a decrease in current for a fixed supply voltage.

Exam Tip: In competitive exams, always remember the mnemonic 'L is for Long/Large Resistance' to quickly identify how length affects circuit parameters.

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