Physics Current Electricity ETEA 2018
PMDC Verified Question 92 of 112
A metal cube with sides of length "a" has electrical resistance R between opposite faces. What is the resistance between the opposite faces of a cube of the same metal with sides of length 3a?
A
9R
B
3R
C
R/3
D
R/9
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: R/3
Concept:

The resistance of a regular solid changes dynamically with its length and cross-sectional area.

Formula:

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

Solution:

  • For the first cube, distance \( L = a \) and area \( A = a \times a = a^2 \). Resistance \( R_1 = \rho \frac{a}{a^2} = \frac{\rho}{a} = R \).


  • For the new larger cube, distance \( L = 3a \) and area \( A = (3a) \times (3a) = 9a^2 \).


  • New Resistance \( R_2 = \rho \frac{3a}{9a^2} = \rho \frac{1}{3a} = \frac{1}{3} \left(\frac{\rho}{a}\right) = \frac{R}{3} \).


Why other options are incorrect:

  • Opt A & B: Occurs if you only scale length and forget to scale the cross-sectional area.


  • Opt D: Occurs if you divide area by length erroneously.

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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