JEE MAIN - Physics (2009 - No. 24)
Statement - 1: The temperature dependence of resistance is usually given as $$R = {R_0}\left( {1 + \alpha \,\Delta t} \right).$$ The resistance of wire changes from $$100\Omega $$ to $$150\Omega $$ when its temperature is increased from $${27^ \circ }C$$ to $${227^ \circ }C$$. This implies that $$\alpha = 2.5 \times {10^{ - 3}}/C.$$
Statement - 2: $$R = {R_0}\left( {1 + \alpha \,\Delta t} \right)$$ is valid only when the change in the temperature $$\Delta T$$ is small and $$\Delta T = \left( {R - {R_0}} \right) < < {R_0}.$$
Statement - 1 is true, Statement - 2 is true; Statement - 2 is the correct explanation of Statement - 1
Statement - 1 is true, Statement - 2 is true; Statement - 2 is not the correct explanation of Statement - 1
Statement - 1 is false, Statement - 2 is true
Statement - 1 is true, Statement - 2 is false
Explanation
The relation $$R = {R_0}\left( {1 + \alpha \,\Delta t} \right)$$ is valid for small values of $$\Delta t$$ and $${R_0}$$ is resistance at $${0^ \circ }C$$ and also $$\left( {R - {R_0}} \right)$$ should be much smaller than $${R_0}.$$ So, statement $$(1)$$ is wrong but statement $$(2)$$ is correct.
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