When subjected to a voltage of 10 , V, the cu | vedclass

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Question

(A) Given: Voltage $V = 10 \, V$, initial current $I_1 = 0.1 \, A$, initial temperature $t_1 = 40^{\circ} C$, and temperature coefficient $\alpha = 2

Vedclass · Accepted Answer

$142$

Vedclass · Answer

(A) Given: Voltage $V = 10 \, V$, initial current $I_1 = 0.1 \, A$, initial temperature $t_1 = 40^{\circ} C$, and temperature coefficient $\alpha = 2 	imes 10^{-4} {}^{\circ} C^{-1}$.The initial resistance $R_1$ at $t_1 = 40^{\circ} C$ is $R_1 = \frac{V}{I_1} = \frac{10}{0.1} = 100 \, \Omega$.The resistance at temperature $t_2$ when the current $I_2 = 0.098 \, A$ is $R_2 = \frac{V}{I_2} = \frac{10}{0.098} \approx 102.04 \, \Omega$.Using the relation $R_2 = R_1 [1 + \alpha(t_2 - t_1)]$:$102.04 = 100 [1 + 2 	imes 10^{-4} (t_2 - 40)]$.$1.0204 = 1 + 2 	imes 10^{-4} (t_2 - 40)$.$0.0204 = 2 	imes 10^{-4} (t_2 - 40)$.$t_2 - 40 = \frac{0.0204}{2 	imes 10^{-4}} = 102$.$t_2 = 102 + 40 = 142^{\circ} C$.

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