GATE 2023 IN – Question 61
The sinusoidal source shown has frequency 50 Hz. The load voltage is 230 V RMS and impedance is $230/\sqrt2+j230/\sqrt2$ Ω. Attenuator $A_1=1/(50\sqrt2)$. The multiplier gives $V_o=V_xV_y/(1\ \mathrm V)$, where $V_x,V_y$ are its inputs. The magnitude of average $V_o$ is ______ V (one decimal place).
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Correct answer: 2.1 to 2.5
Explanation
The load impedance magnitude is 230 Ω, so current is 1 A RMS with 45° lag. The 1 Ω shunt gives 1 V RMS. The attenuated load voltage is $230/(50\sqrt2)$ V RMS; advancing it 90° puts it 135° from current. Mean-product magnitude is $[230/(50\sqrt2)]|\cos135^\circ|=\boxed{2.3}$ V.