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The resistance of a bulb filament is $100 \Omega$ at a temperature of $100^{\circ} \mathrm{C}.$ if its temperature coefficiest of resistance is $0.005 / 0 \mathrm{C}.$ $0.005 /^0 \mathrm{C}.$ its resistance will become $200 \Omega$ at a temperature of.
Option: 1
$500^0C$

Option: 2
$200^0C$

Option: 3
$300^0C$

Option: 4
$400^0C$

Answers (1)

best_answer

$R_t=R_0(1+\alpha t)$

Here, $R_t=100^{\circ} \mathrm{C}, \alpha=0.005, \quad t=100$

So, $R_t=R_0(1+0.005(100))$

$\begin{aligned} & \Rightarrow 100=R_0(1+0.5) \\ & \Rightarrow R_0=\frac{100}{4.5}=\frac{100 \times 2}{3}=\frac{200}{3} \Omega--(1) \end{aligned}$

and at $t$ temperature at which resistance becomes $200 \Omega$

$R_t=R_0(1+0.005 t)$

$\begin{aligned} & \Rightarrow 200=\frac{200}{3}(1+0.005 t) \\ & \Rightarrow \frac{3 \times 200}{200}=1+0.005 t \end{aligned}$

$\begin{aligned} & \Rightarrow \quad 3=1+0.005 t \\ & \Rightarrow \quad t=\frac{3-1}{0.005}=\frac{.2}{0.005}=\frac{2000}{5}=400^{\circ} \mathrm{C} \end{aligned}$

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sudhir kumar

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