Physics Current Electricity KU 2024
PMDC Verified Question 10 of 112
If \(R_1\) and \(R_2\) are respectively the filament resistance of a 100-Watt bulb and 200-Watt bulb designed to operate on the same voltage, then:
A
\(R_1\) is two times \(R_2\)
B
\(R_2\) is two times \(R_1\)
C
\(R_2\) is four times \(R_1\)
D
\(R_1\) is four times \(R_2\)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: \(R_1\) is two times \(R_2\)
Concept:

When components are designed to operate at the same nominal voltage, their internal resistance heavily dictates their power draw.

Formula:

$$ P = \frac{V^2}{R} \implies R = \frac{V^2}{P} $$

Solution:

  • Resistance is inversely proportional to Power rating (\( R \propto 1/P \)).


  • Let's take the ratio: \( \frac{R_1}{R_2} = \frac{P_2}{P_1} \).


  • \( \frac{R_1}{R_2} = \frac{200}{100} = 2 \).


  • Therefore, \( R_1 = 2 R_2 \). The 100W bulb has exactly two times the resistance of the 200W bulb.


Why other options are incorrect:

  • Opt B: Assumes resistance is directly proportional to power.


  • Opt C & D: Assumes a squared relationship which doesn't exist here.

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