JEE MAIN - Physics (2021 - 27th July Evening Shift - No. 18)
The resistance of a conductor at 15$$^\circ$$C is 16$$\Omega$$ and at 100$$^\circ$$C is 20$$\Omega$$. What will be the temperature coefficient of resistance of the conductor?
0.010$$^\circ$$C$$-$$1
0.033$$^\circ$$C$$-$$1
0.003$$^\circ$$C$$-$$1
0.042$$^\circ$$C$$-$$1
Explanation
16 = R0 [1 + $$\alpha$$ (15 $$-$$ T0)]
20 = R0 [1 + $$\alpha$$ (100 $$-$$ T0)]
Assuming T0 = 0$$^\circ$$C, as a general convention.
$$\Rightarrow$$ $${{16} \over {20}} = {{1 + \alpha \times 15} \over {1 + \alpha \times 100}}$$
$$\Rightarrow$$ $$\alpha$$ = 0.003$$^\circ$$C$$-$$1
20 = R0 [1 + $$\alpha$$ (100 $$-$$ T0)]
Assuming T0 = 0$$^\circ$$C, as a general convention.
$$\Rightarrow$$ $${{16} \over {20}} = {{1 + \alpha \times 15} \over {1 + \alpha \times 100}}$$
$$\Rightarrow$$ $$\alpha$$ = 0.003$$^\circ$$C$$-$$1
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