Physics Current Electricity ETEA 2022
PMDC Verified Question 62 of 112
A conductor has length equal to \(\pi\) meters and radius r meters. Its resistance will be equal to:
A
\( R = \rho r^{-1} \)
B
\( R = \rho r^{-2} \)
C
\( R = \rho r^{-3} \)
D
\( R = \rho r^{2} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: \( R = \rho r^{-2} \)
Concept:

Calculate resistance by substituting physical values into the standard resistivity formula.

Formula:

$$ R = \rho \frac{L}{A} $$

Solution:

  • Length \( L = \pi \).


  • Cross-sectional Area \( A = \pi r^2 \).


  • Substitute values: \( R = \rho \frac{\pi}{\pi r^2} \).


  • The \(\pi\) cancels out: \( R = \frac{\rho}{r^2} \).


  • Written with a negative exponent: \( R = \rho r^{-2} \).


Why other options are incorrect:

  • Opt A, C, D: Feature incorrect algebraic simplifications of the denominator \( r^2 \).

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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