GATE 2023 EE – Question 51
For the circuit shown, if $i=\sin1000t$, the instantaneous value of the Thevenin’s equivalent voltage (in Volts) across the terminals $a$-$b$ at time $t=5$ ms is ___________ (Round off to 2 decimal places).
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Correct answer: -12.05 to -11.93
Explanation
Use phasors ($\omega=1000$, $I=1\angle0^\circ$). With $a$-$b$ open, the current $i_x$ flows from the dependent source down through $10\ \Omega$ and $-j10\ \Omega$ to $b$, so $V_{ab}=i_x(10-j10)$. The source current splits between the $(10+j10)\ \Omega$ branch and the path through the dependent source: $I_{right}=1-i_x$. KVL: $i_x(10-j10)=(1-i_x)(10+j10)+4i_x$, so $i_x(6-j10+10+j10)\cdot$ ... $i_x=\dfrac{10+j10}{16}$ and $V_{ab}=\dfrac{(10+j10)(10-j10)}{16}=12.5$ V, i.e. $12.5\sin1000t$. At $t=5$ ms, $\sin(5\text{ rad})=-0.9589$, so $v_{th}=-11.99$ V.