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.
This question appeared on the ETEA MDCAT 2013 paper, which you can sit online with every answer explained.
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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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