GATE 2023 IN – Question 55
A 4 H inductor carries $i_1(t)=\sin(200\pi t)$ mA and is mutually coupled to a 5 H inductor carrying $i_2(t)=2\sin(200\pi t)$ mA, with dot polarities shown. The coupling coefficient is 0.6. Peak stored energy is ______ μJ (two decimal places).
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Correct answer: 17.00 to 18.00
Explanation
Both currents enter dotted terminals, so mutual energy is positive. $M=k\sqrt{L_1L_2}=0.6\sqrt{20}=2.6833$ H. At simultaneous peaks, $W=\tfrac12(4)(0.001)^2+\tfrac12(5)(0.002)^2+M(0.001)(0.002)=\boxed{17.37}$ μJ.