By how many times does doubling the diameter of a wire and making it 10 times longer increase its resistance?
Correct answer: A. 2.5 times
- A. 2.5 times
- B. 5 times
- C. 10 times
- D. 30 times
Explanation
The Resistance of a wire is calculated asR = P L/Awhere R = resitance of the wireL = Length of the wireA is the area of the wire = (pi d2)/4P = resistivity of the materialR1 = 4 P L /(pi d2)R2 = 4 P 10L /(pi (2 d)2)R2/R1 = 10/4 = 2.5 ANS
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About Resistance and Resistivity
Resistance measures opposition to current in a conductor and follows R = V/I for an ohmic conductor, while resistivity is an intrinsic property of the material. Questions use R = ρL/A, examine effects of length, cross-sectional area and temperature, and distinguish resistance, resistivity, conductance and conductivity.
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