The resistance of wire at $0^{\circ} \mathrm{C}$ is $20 \Omega$. If the temperature coefficient of the…

The resistance of wire at $0^{\circ} \mathrm{C}$ is $20 \Omega$. If the temperature coefficient of the resistance is $5 \times 10^{-3}{ }^{\circ} \mathrm{C}^{-1}$. The temperature at which the resistance will be double of that at $0^{\circ} \mathrm{C}$ is
  1. $10^{\circ} \mathrm{C}$
  2. $200^{\circ} \mathrm{C}$
  3. $250^{\circ} \mathrm{C}$
  4. $300^{\circ} \mathrm{C}$

Solution

Resistance of wire at $0^{\circ} \mathrm{C}, R_0=20 \Omega$ Temperature coefficient, $\begin{aligned} & \alpha=5 \times 10^{-3}{ }^{\circ} \mathrm{C}^{-1} \\ & R_t=2 R_0=2 \times 20=40 \Omega\end{aligned}$ we know that, $R_t=R_0(1+\alpha t)$ $\Rightarrow \quad 40=20\left(1+5 \times 10^{-3} t\right) \Rightarrow 2=1+5 \times 10^{-3} t$ $\Rightarrow \quad t=\frac{1}{5 \times 10^{-3}}=\frac{1000}{5}=200^{\circ} \mathrm{C}$

Asked in: AP EAMCET 2022 (05 Jul Shift 1)

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