NEET Physics Question - Current Electricity - Variation of Resistance with Temperature

Assertion (A): In \(R = R_0(1 + \alpha\Delta T)\) when temp. is increased from \(27^\circ C\) to \(227^\circ C\) resistance increases from \(100 \Omega\) to \(150 \Omega\) this implies \(\alpha = 2.5 \times 10^{-3} /^{\circ} C\).

Reason (R): (R = R_0(1 + \alpha\Delta T)\) is valid only when change in temp \(\Delta T\) is very small i.e. \(\Delta R = (R-R_0) \ll R_0\).

Both (A) & (R) are true and the (R) is the correct explanation of the (A)

Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

(A) is true but (R) is false

Both (A) and (R) are false

Solution:

For (A): \(\Delta T = 227 - 27 = 200^\circ C\). Given \(R=150 \Omega\) and \(R_0=100 \Omega\). Using \(R = R_0(1 + \alpha\Delta T)\) \(\Rightarrow 150 = 100(1 + \alpha \times 200)\) \(\Rightarrow 1.5 = 1 + 200\alpha\) \(\Rightarrow 0.5 = 200\alpha\) \(\Rightarrow \alpha = 2.5 \times 10^{-3} /^{\circ} C\). So, (A) is true. For (R): The formula \(R = R_0(1 + \alpha\Delta T)\) is an empirical approximation for temperature dependence of resistance. It is often used for significant temperature changes and is not strictly limited to very small \(\Delta T\) or \(\Delta R \ll R_0\). Thus, (R) is false.

Rankers Physics

Temperature Dependence of Resistance

Solution:

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