In the circuit shown the resistance R is kept in a chamber whose temperature is 2 0 ∘ C which remains constant. The initial temperature and resistance of R is 5 0 ∘ C and 15Ω respectively. The rate of

Question

In the circuit shown the resistance R is kept in a chamber whose temperature is $2 0^{\circ} C$ which remains constant. The initial temperature and resistance of R is $5 0^{\circ} C$ and $15Ω$ respectively. The rate of change of resistance R with temperature is $1/2$ $Ω/^{\circ} C$ and rate of decrease of temperature of R is $\frac{( l n 3 )}{100}$ times the temperature difference from surrounding. Assume the resistance R loses heat only in accordance with Newton's law of cooling. If both keys are closed at $t = 0$ .

TestHub · Accepted Answer

For P: So, power is maximum when R is 5 Ω . For Q: R is 5 Ω when the drop in temperature is 2 0 ∘ C , so the temperature is 3 0 ∘ C . For R: − dt d θ ​ = 100 l n 3 ​ ( θ − 2 0 ∘ ) For S: ∫ 5 0 ∘ 3 0 ∘ ​ − ( θ − 2 0 ∘ ) d θ ​ = 100 l n 3 ​ ∫ 0 t ​ d t t = 100 sec . By applying the loop law, we can calculate the current when R is 5 Ω .

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