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PhysicsCurrent ElectricityEquivalent ResistanceEasy2 minPYQ_2017

PhysicsEasysingle choice

The resistance of a wire at $20 ° C$ is $20 Ω$ and $500 ° C$ is $60 Ω$ . At which temperature, its resistance will be $25 Ω ?$

Answer:

Solution:

We have, $R_{t} = R_{0} (1 + α t)$

Here, $20 = R_{0} (1 + 20 α)$

$60 = R_{0} (1 + 500 α)$

$\Rightarrow \frac{60}{20} = \frac{R_{0} (1 + 500 α)}{R_{0} (1 + 20 α)}$

$3 = \frac{1 + 500 α}{1 + 20 α}$

$\Rightarrow 3 (1 + 20 α) = 1 + 500 α$

$\Rightarrow 3 + 60 α = 1 + 500 α$

$\Rightarrow 440 α = 2$

$\Rightarrow α = \frac{2}{440} = \frac{1}{220} I ° C$

Also given $R_{t} = 25 ° C, t = ?$

Now, $\frac{20}{25} = \frac{R_{0} (1 + \frac{20}{220})}{R_{0} (1 + \frac{t}{220})}$

$4 (1 + \frac{t}{220}) = 5 (1 + \frac{20}{220})$

On solving,

$t = 80 ° C$

Stream:BITSATSubject:PhysicsTopic:Current ElectricitySubtopic:Equivalent Resistance

⏱ 2mℹ️ Source: PYQ_2017

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