Physics Current Electricity NUMS 2020
PMDC Verified Question 85 of 112
If length of the wire becomes two time to the original value and area becomes one half to its original value, then resistance of the wire becomes:
A
Double
B
Four times
C
One half
D
One fourth
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: Four times
Concept:

Resistance is directly proportional to length and inversely proportional to cross-sectional area.

Formula:

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

Solution:

  • Original resistance: \( R \).


  • New Length \( L' = 2L \).


  • New Area \( A' = \frac{A}{2} \).


  • New Resistance \( R' = \rho \frac{2L}{A/2} = 4 \left( \rho \frac{L}{A} \right) = 4R \).


  • The resistance becomes four times greater.


Why other options are incorrect:

  • Opt A: Occurs if you only double the length and ignore the area change.


  • Opt C & D: Occurs if relations are applied inversely.

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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