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The electrical resistance of a metallic wire is inversely proportional to its ________.
Length
Resistivity
Cross-sectional area
Temperature
Cross-sectional area
The electrical resistance of a metallic conductor is inversely proportional to its cross-sectional area. As the area increases, there is more space for electrons to flow, thereby reducing the opposition to the current.
The electrical resistance of a metallic conductor is inversely proportional to its cross-sectional area. As the area increases, there is more space for electrons to flow, thereby reducing the opposition to the current.
Think of a wire like a water pipe: a wider pipe allows more water to flow with less friction than a narrow pipe, just as a thicker wire allows more current to flow with less electrical resistance.
Remember 'Thick wire, low resistance' (Area up, Resistance down).
R=╧БAlтАЛ тАФ Ohm's law relation for geometry, where R is resistance, ╧Б is resistivity, l is length, and A is cross-sectional area.
According to the fundamental law of resistance, R=╧БAlтАЛ, where R is resistance, ╧Б is resistivity, l is length, and A is the cross-sectional area. Since RтИЭA1тАЛ, doubling the area cuts the resistance in half because more charge carriers (electrons) can pass through the wire simultaneously at a given time.
Resistance is directly proportional to the length of the wire (RтИЭl).
Resistance is inversely proportional to the cross-sectional area (RтИЭA1тАЛ).
Resistivity (╧Б) is a property of the material itself and is independent of dimensions.
Resistance increases with an increase in temperature for metallic conductors.
Using thicker wires for high-current appliances minimizes power loss due to heat.
Increased thickness leads to higher weight and higher material cost in electrical cabling.
Power transmission lines use varying thicknesses based on current requirements.
Fuses use thinner wires to ensure higher resistance, causing them to melt at a specific current threshold.
Resistivity (╧Б) depends only on the nature of the material and temperature.
Option A is incorrect because resistance is directly proportional to length.
Option B is incorrect because resistivity is an intrinsic material property independent of geometry.
Option D is incorrect because resistance in metals is directly (not inversely) proportional to temperature changes.
C is correct тАФ The resistance of a conductor is inversely proportional to its cross-sectional area (RтИЭA1тАЛ).
Always remember that resistivity is independent of shape/size; it is a material constant. Geometry (length and area) only affects resistance, not resistivity.