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Question
Two wires of equal cross sectional area , one of copper and other of manganinhave same resistance. Which one will be longer?
have same resistance. Which one will be longer?
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Solution
Resistivity of copper is = 1.68 × 10-8 Ωm
Resistivity of manganin is = 48.2 × 10-8 Ωm
Let the length of copper be ‘L’ and that of manganin wire be ‘l’. Their resistance is R and the area of cross-section is A.
Using,
R = ρL/A
=> (1.68 × 10-8)L/A = (48.2 × 10-8)l/A
=> L/l = 48.2/1.68
=> L/l > 1
=> L > l
Thus, the copper wire is longer than the manganin wire.
Resistivity of copper is = 1.68 × 10-8 Ωm
Resistivity of manganin is = 48.2 × 10-8 Ωm
Let the length of copper be ‘L’ and that of manganin wire be ‘l’. Their resistance is R and the area of cross-section is A.
Using,
R = ρL/A
=> (1.68 × 10-8)L/A = (48.2 × 10-8)l/A
=> L/l = 48.2/1.68
=> L/l > 1
=> L > l
Thus, the copper wire is longer than the manganin wire.
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