The circuit has steady-state output y(t)=A()[ t+()]. For A() =0.25, find ω.

GATE 2014 EC (EC4) – Question 40

Networks, Signals and Systems · Sinusoidal Steady State Analysis · 2 marks · Multiple choice

The circuit has steady-state output $y(t)=A(\omega)\sin[\omega t+\phi(\omega)]$. For $|A(\omega)|=0.25$, find ω.

Diagram for GATE 2014 EC (EC4) question 40

$1/(\sqrt3RC)$
$2/(\sqrt3RC)$
$1/(RC)$
$2/(RC)$

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Show answer and explanation

Correct answer: (B) $2/(\sqrt3RC)$

Explanation

The two right capacitors in series have capacitance C/2, in parallel with the middle C, so total load is3C/2. Their midpoint divides the node voltage equally; output across the upper right capacitor is half the node voltage. Thus |A|=(1/2)/√[1+(3ωRC/2)²]. Setting it to1/4gives3ωRC/2=√3, hence **ω=2/(√3RC),B**.