GATE 2014 EC (EC3) – Question 40

Networks, Signals and Systems · Time and Frequency Domain Analysis of Linear Circuits · 2 marks · Multiple choice

Network N shown has C = 100 µF and R = 10 kΩ. Two such blocks are cascaded as shown. Find V₃(s)/V₁(s).

Diagram for GATE 2014 EC (EC3) question 40

$s/(1+s)$
$s^2/(1+3s+s^2)$
$(s/(1+s))^2$
$s/(2+s)$

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Correct answer: (B) $s^2/(1+3s+s^2)$

Explanation

RC=10kΩ×100µF=1s. With intermediate voltage V2 and output V3, output-node KCL gives s(V3−V2)+V3=0, so V2=(s+1)V3/s. Intermediate KCL is s(V2−V1)+V2+s(V2−V3)=0. Eliminating V2 gives **V3/V1=s²/(s²+3s+1),B**. Squaring the isolated-block gain ignores loading.