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  4. A coil of self inductance L=1 H resistance r=4 Ω is connected in series with a variable resistance R and an a.c. source with ω =3 rad/sec as shown in figure. What should be the value of R (in Ω ) so that rate of heat loss through R is maximum? <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-oyy9aqgtj69vxymu.jpg />

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Q. A coil of self inductance $L=1\,H$ & resistance $r=4\,\Omega$ is connected in series with a variable resistance $R$ and an a.c. source with $\omega =3\,rad/sec$ as shown in figure. What should be the value of $R$ (in $\Omega$ ) so that rate of heat loss through $R$ is maximum?
Question

NTA AbhyasNTA Abhyas 2022

Solution:

$H=i^{2}R=\left(\frac{V_{0}}{\sqrt{\left(R + r\right)^{2} + \left(\omega L\right) ^{2}}}\right)^{2}\times R$ for maximum value of $H$ solve $\frac{d H}{d R}=0$
On solving $R=5\,\Omega$