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Which of the following statements are true with regard to resistance?
Resistance is directly proportional to a length of the wire
Resistance is directly proportional to an area of cross-section of the wire
Resistance is inversely proportional to the length of the wire
Resistance is inversely proportional to the resistivity of the wire
Resistance is directly proportional to a length of the wire
The electrical resistance R of a uniform conductor is directly proportional to its length l and inversely proportional to its cross-sectional area A. This relationship is defined by the formula R=╧БAlтАЛ, where ╧Б is the resistivity of the material.
The electrical resistance R of a uniform conductor is directly proportional to its length l and inversely proportional to its cross-sectional area A. This relationship is defined by the formula R=╧БAlтАЛ, where ╧Б is the resistivity of the material.
R=╧БAlтАЛ тАФ Resistance formula where ╧Б is resistivity, l is length, and A is area.
╧Г=╧Б1тАЛ тАФ Conductivity is the reciprocal of resistivity.
As the length of a wire increases, the number of electron collisions with ions in the crystal lattice increases, leading to higher resistance. Conversely, increasing the cross-sectional area provides more paths for charge carriers, thereby reducing the effective resistance of the material.
Resistance increases linearly with length (RтИЭl).
Resistance decreases as cross-sectional area increases (RтИЭA1тАЛ).
Resistivity (╧Б) is a property of the material and does not change with geometry.
Predictable circuit behavior
Uniform current distribution in homogeneous materials
Resistance changes with temperature (╬▒ coefficient)
Skin effect at high frequencies reduces effective cross-sectional area
Resistor manufacturing
Power transmission lines design
Option B is incorrect because RтИЭA1тАЛ.
Option C is incorrect because R is directly, not inversely, proportional to length.
Option D is incorrect because R is directly proportional to resistivity (╧Б).
A is correct тАФ Resistance is directly proportional to the length of the wire, consistent with the fundamental relation R=╧БAlтАЛ.
Always remember the mnemonic 'Longer wires have more resistance, fatter wires have less resistance' for quick analysis in DC circuit problems.