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What happens to the resistance of a conductor if its length is doubled and area of cross-section is halved?
Remains same
Becomes 2 times
Becomes 4 times
Becomes 1/4 times
Becomes 4 times
The resistance of a conductor is directly proportional to its length and inversely proportional to its cross-sectional area. When the length is doubled and the area is halved, the resistance increases by a factor of four.
The resistance of a conductor is directly proportional to its length and inversely proportional to its cross-sectional area. When the length is doubled and the area is halved, the resistance increases by a factor of four.
Think of a water pipe: making the pipe twice as long makes it harder for water to flow through (more resistance), and making it half as thin further restricts the flow, compounding the difficulty significantly.
L-A-R: Length Above, Area under Resistance (Length numerator, Area denominator)
R=╧БAlтАЛ тАФ Formula relating resistance, resistivity, length, and cross-sectional area
RтА▓=4R тАФ Scaled resistance calculation for doubled length and halved area
According to the resistance formula R=╧БAlтАЛ, where R is resistance, ╧Б is resistivity, l is length, and A is cross-sectional area, doubling the length (lтА▓=2l) and halving the area (AтА▓=2AтАЛ) results in a new resistance RтА▓=╧БA/22lтАЛ=4╧БAlтАЛ=4R.
Resistance is directly proportional to the length of the conductor (RтИЭl).
Resistance is inversely proportional to the cross-sectional area of the conductor (RтИЭA1тАЛ).
Resistivity (╧Б) is a material property and remains constant regardless of dimensions.
Design of electrical transmission lines
Selection of appropriate resistor dimensions in electronic circuits
Resistivity depends only on the material and temperature, not on the shape or size of the conductor.
Option A is incorrect because changing dimensions alters the resistance. Option B accounts only for the length change. Option D inverts the area relationship.
C is correct тАФ The resistance becomes 4 times the original value when the length is doubled and the cross-sectional area is halved.
Always check whether dimensions are given as radius or diameter when calculating the cross-sectional area (A=╧Аr2 or A=4╧Аd2тАЛ). Changes in radius square the effect on area!