Temperature coefficient of resistance is expressed in terms of

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ohms/ohms degree centigrade Explanation: The temperature coefficient of resistance ($\alpha$) defines the fractional change in resistance per unit change in temperature. Since it represents the ratio of change in resistance ($\Omega$) to the product of initial resistance ($\Omega$) and temperature change ($^{\circ}C$), its unit is $\Omega / (\Omega \cdot ^{\circ}C)$, which simplifies to $^{\circ}C^{-1}$. Working Principle: As temperature increases, the atomic vibrations in a conductive material increase, leading to more frequent collisions between charge carriers and the crystal lattice. This process restricts electron flow, causing the resistance to vary linearly with temperature according to the relation $R_t = R_0(1 + \alpha_0 \Delta T)$. Rearranging this for $\alpha$ yields $\alpha = \frac{R_t - R_0}{R_0 \Delta T}$, resulting in the unit $\frac{\Omega}{\Omega \cdot ^{\circ}C}$. Key Formulas: $R_t = R_0(1 + \alpha_0 \Delta T)$ — Resistance at temperature $t$; $\alpha_0 = \frac{R_t - R_0}{R_0 \Delta T}$ — Definition of temperature coefficient Key Points: The unit $\Omega / (\Omega \cdot ^{\circ}C)$ is dimensionally equivalent to $1/^{\circ}C$ or $^{\circ}C^{-1}$.; Positive temperature coefficient (PTC) is typical for most metals.; Negative temperature coefficient (NTC) is observed in semiconductors and electrolytes.; The coefficient is usually defined with respect to a reference temperature, often $0^{\circ}C$ or $20^{\circ}C$. Advantages: Predicts component behavior in varying thermal environments; Essential for designing precision instrumentation and thermal sensors Disadvantages: Requires calibration at specific reference temperatures; Non-linear effects can occur at extreme temperature ranges Applications: Resistance Temperature Detectors (RTD); Thermal compensation in electronic circuits Additional Info: The units given in the options are written as 'ohms/ohms degree centigrade', which is a descriptive way of writing $\Omega / (\Omega \cdot ^{\circ}C)$.. Option B (mhos/ohm degree centigrade) is incorrect because mhos are units of conductance, not resistance. Answer: A is correct — The temperature coefficient of resistance has units of $\Omega / (\Omega \cdot ^{\circ}C)$, indicating a fractional change in resistance per degree of temperature. Exam Tip: Remember that resistance and resistivity have the same temperature coefficient property; if the material is constant, the coefficient depends on the atomic structure, not the physical dimensions of the conductor.

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