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How is the resistance of a wire related to the length of the wire?
Inversely proportional
Proportional to square of length
Directly proportional
Not related
Directly proportional
The electrical resistance of a metallic wire is directly proportional to its length l. This means that if the length of a wire is doubled, keeping the cross-sectional area and material constant, its resistance will also double.
The electrical resistance of a metallic wire is directly proportional to its length l. This means that if the length of a wire is doubled, keeping the cross-sectional area and material constant, its resistance will also double.
Think of electrical resistance like walking through a crowded hallway; the longer the hallway, the more people you bump into, making it harder and more time-consuming to reach the end.
L-R Direct: Length goes up, Resistance goes up.
R=╧БAlтАЛ тАФ where R is resistance, ╧Б is resistivity, l is length, and A is cross-sectional area.
RтИЭl тАФ shows the direct proportionality between resistance and length.
Resistance arises due to the collisions between moving electrons and the atoms of the conductor. As the length of the wire increases, an electron moving through the conductor encounters more atoms, leading to a greater number of collisions. Therefore, a longer path provides more cumulative resistance to the flow of current.
Resistance is the opposition to the flow of electric current.
Resistivity (╧Б) is an intrinsic property of the material and does not change with length.
The SI unit of resistance is the Ohm (╬й).
Used in designing rheostats for controlling current flow.
Essential for calculating voltage drop in long-distance power transmission cables.
Resistance is also inversely proportional to the area of cross-section (RтИЭA1тАЛ).
Option A is incorrect because resistance does not decrease as length increases.
Option B is incorrect because resistance is linear, not quadratic, with respect to length.
C is correct тАФ Resistance is directly proportional to the length of the wire, meaning RтИЭl.
Always remember that resistance depends on the geometry of the conductor (length, area) and its intrinsic material property (resistivity), not on the voltage or current applied.
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