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How does the resistance of a metallic conductor change if its length is doubled while keeping the area of cross-section constant?
Remains the same
Doubles
Halves
Becomes four times
Doubles
The resistance of a metallic conductor is directly proportional to its length. When the length of the conductor is doubled while keeping its cross-sectional area and material constant, its resistance also doubles.
The resistance of a metallic conductor is directly proportional to its length. When the length of the conductor is doubled while keeping its cross-sectional area and material constant, its resistance also doubles.
Think of a water pipe: a longer pipe offers more resistance to water flow than a shorter pipe of the same width, making it twice as hard to push water through if the pipe length is doubled.
R=A╧БlтАЛ тАФ Formula for electrical resistance
RтИЭl тАФ Resistance is directly proportional to length
According to the law of resistance, R=A╧БlтАЛ, where R is resistance, ╧Б is resistivity, l is length, and A is cross-sectional area. Doubling the length l increases the path length for electron flow proportionally, thereby doubling the resistance.
Resistance is directly proportional to the length of the conductor.
Resistance is inversely proportional to the cross-sectional area of the conductor.
Resistivity (╧Б) depends only on the material and temperature, not on dimensions.
Designing heating elements where length determines total resistance.
Calculating line losses in long-distance electrical transmission lines.
Resistivity (╧Б) remains unaffected by changes in length or cross-sectional area.
Option A is incorrect because resistance depends on dimensions. Option C describes halving the length. Option D describes quadrupling, which happens when length is quadrupled or area is quartered.
B is correct тАФ The resistance of a metallic conductor doubles when its length is doubled because resistance is directly proportional to length (RтИЭl).
Always check whether dimensions are stretched (keeping volume constant) or simply extended, as stretching alters both length and area simultaneously!
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