A wire has a resistance 'R'. If its length is doubled and radius is reduced to half then its resistance will become:
Correct answer: C. 8R
- A. 2R
- B. 4R
- C. 8R
- D. 16R
Explanation
To determine the new resistance, use the formula Resistance = resistivity × length/area. When the length is doubled, the resistance is also doubled (2R). Reducing the radius to half causes the cross-sectional area (πr²) to become one quarter, which increases the resistance by a factor of four (4R). Therefore, the new resistance is 2 × 4 = 8R. Options 2R and 4R underestimate the effect of reducing the radius, while 16R overestimates it.
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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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