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The resistance of a 10 m long copper wire is R ohm. What will be the resistance of a 5 m long copper wire?
0.5R ohm
R ohm
5R ohm
2R ohm
0.5R ohm
The resistance of a uniform conductor is directly proportional to its length (RтИЭl). When the length of the copper wire is halved from 10 m to 5 m, its resistance also becomes half, which is 0.5R┬аohm.
The resistance of a uniform conductor is directly proportional to its length (RтИЭl). When the length of the copper wire is halved from 10 m to 5 m, its resistance also becomes half, which is 0.5R┬аohm.
Think of a water pipe: a longer pipe offers more resistance to water flow than a shorter pipe of the same diameter. If you cut the pipe in half, the resistance to water flow through that section is also cut in half.
Longer length, larger resistance; shorter length, smaller resistance.
R=╧БAlтАЛ тАФ Resistance formula in terms of length and cross-sectional area
RтИЭl тАФ Resistance is directly proportional to length for a uniform wire
According to the laws of electrical resistance, the resistance R of a conductor of uniform cross-sectional area A and length l is given by the formula R=╧БAlтАЛ, where ╧Б is the resistivity of the material. Since the material (copper), cross-sectional area, and temperature remain constant, the resistance is directly proportional to the length (RтИЭl). Therefore, if length l becomes 2lтАЛ, the new resistance becomes 2RтАЛ or 0.5R.
Electrical resistance is directly proportional to the length of the conductor.
Electrical resistance is inversely proportional to the cross-sectional area of the conductor.
Resistivity (╧Б) depends only on the nature of the material and temperature, not on dimensions.
When length is halved, resistance is also halved.
Direct linear relationship makes calculations simple.
Crucial principle in designing transmission lines and rheostats.
Volume control potentiometers and dimmer switches.
Resistance thermometers (RTDs) measuring temperature changes via resistance variation.
Unit of resistance is Ohm (╬й).
Copper is widely used due to its low resistivity and high conductivity.
A is correct тАФ The resistance of a wire is directly proportional to its length (RтИЭl), so cutting the length in half halves the resistance to 0.5R┬аohm
Always check if the wire is stretched or cut. If a wire is stretched to n times its length, its resistance increases by n2 times due to volume conservation (RтИЭl2). If it is simply cut, RтИЭl directly.