Question

What happens to resistance if the length of the conductor is increased?

• A. \( \text{Decreases} \)
• B. \( \text{No change} \)
• C. \( \text{Increases} \)
• D. \( \text{Doubles} \)

Hint:

Think of it like a long road. The longer the road (conductor), the more effort (resistance) it takes for a car (electron) to travel from one end to the other. Conversely, a wider road (larger cross-sectional area) makes it easier for traffic, thus decreasing resistance.

Answer 1

The Correct Option is C

The electrical resistance ($R$) of a conductor is directly proportional to its length ($L$) and inversely proportional to its cross-sectional area ($A$). This relationship is described by the formula: $$R = \rho \frac{L}{A}$$ Where:

• $R$ is the resistance in ohms ($\Omega$)
• $\rho$ (rho) is the resistivity of the material in ohm-meters ($\Omega \cdot m$), which is a property of the material itself and remains constant for a given material at a constant temperature.
• $L$ is the length of the conductor in meters ($m$)
• $A$ is the cross-sectional area of the conductor in square meters ($m^2$)

From this formula, it is clear that if the length ($L$) of the conductor is increased, assuming the resistivity ($\rho$) and the cross-sectional area ($A$) remain constant, the resistance ($R$) will also increase proportionally. This is because a longer conductor provides more obstacles for the free electrons to flow through, leading to more collisions and thus higher resistance.