The resistance of a wire at 0^{circ} C is 20 | vedclass

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(B) Given: Resistance at $0^{\circ} C$ is $R_0 = 20 \Omega$.Temperature coefficient of resistance is $\alpha = 5 	imes 10^{-3} {}^{\circ} C^{-1}$.We

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$200$

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(B) Given: Resistance at $0^{\circ} C$ is $R_0 = 20 \Omega$.Temperature coefficient of resistance is $\alpha = 5 	imes 10^{-3} {}^{\circ} C^{-1}$.We want to find the temperature $t$ at which the resistance $R_t$ becomes double the initial resistance,so $R_t = 2 R_0 = 2 	imes 20 = 40 \Omega$.The formula for resistance at temperature $t$ is $R_t = R_0(1 + \alpha t)$.Substituting the values: $40 = 20(1 + 5 	imes 10^{-3} t)$.Dividing both sides by $20$: $2 = 1 + 5 	imes 10^{-3} t$.Subtracting $1$ from both sides: $1 = 5 	imes 10^{-3} t$.Solving for $t$: $t = \frac{1}{5 	imes 10^{-3}} = \frac{1000}{5} = 200^{\circ} C$.

The resistance of a wire at $0^{\circ} C$ is $20 \Omega$. If the temperature coefficient of resistance is $5 \times 10^{-3} {}^{\circ} C^{-1}$,the temperature at which the resistance will be double that at $0^{\circ} C$ is: (in $^{\circ} C$)

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