Physics Current Electricity MDCAT 2008
PMDC Verified Question 111 of 112
A wire has resistance 100 Ohm at 0 \(^\circ\text{C}\) and 200 Ohm at 100 \(^\circ\text{C}\). What is its temperature coefficient in \(\text{K}^{-1}\)?
A
-0.01
B
0.01
C
-1/273
D
1/273
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: 0.01
Concept:

The temperature coefficient of resistance (\(\alpha\)) represents the fractional change in resistance per degree change in temperature.

Formula:

$$ \alpha = \frac{R_t - R_0}{R_0 \, t} $$

Solution:

  • Initial Resistance \( R_0 = 100 \, \Omega \)


  • Final Resistance \( R_t = 200 \, \Omega \)


  • Change in Temp \( t = 100 \, ^\circ\text{C} \)


  • Substituting the values: \( \alpha = \frac{200 - 100}{100 \times 100} = \frac{100}{10000} = 0.01 \, \text{K}^{-1} \)


Why other options are incorrect:

  • Opt A: Incorrect negative sign; resistance increased, so \(\alpha\) is positive.


  • Opt C/D: These correspond to the volume expansion coefficient of ideal gases (Charles's Law), not the specific wire's resistance.

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