Physics Current Electricity ETEA 2022
PMDC Verified Question 60 of 112
A conductor has resistance R. If its length is stretched to twice the actual value and its radius is reduced to one third of its original values, the new resistance will be:
A
3R
B
9R
C
18R
D
27R
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: 18R
Concept:

Resistance changes drastically when both length and radius are altered.

Formula:

$$ R = \rho \frac{L}{\pi r^2} $$

Solution:

  • Original Resistance: \( R = \rho \frac{L}{\pi r^2} \).


  • New Length \( L' = 2L \).


  • New radius \( r' = \frac{r}{3} \).


  • New Area \( A' = \pi (r')^2 = \pi \left(\frac{r}{3}\right)^2 = \frac{\pi r^2}{9} = \frac{A}{9} \).


  • New Resistance \( R' = \rho \frac{2L}{A/9} = 18 \left(\rho \frac{L}{A}\right) = 18R \).


Why other options are incorrect:

  • Opt A & B: Arise from failing to square the radius reduction factor or failing to multiply by the new doubled length.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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