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GATE 2020 IN – Question 59

Electrical Circuits and Machines · Circuit laws and network theorems: Independent, dependent, ideal and practical sources, Kirchhoff's laws, mesh and nodal analysis, star-delta transformation, superposition, Thevenin's, Norton's, Miller's, maximum power transfer and reciprocity theorems · 2 marks · Numerical answer

The capacitor network, DC source and amplifier of gain G = −5 are shown. Find effective capacitance between A and B in μF, to two decimal places.

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Correct answer: 14.5 to 15.0

Explanation

The 2 μF capacitor bridges amplifier input and output. Miller’s theorem gives its input equivalent $C_M=C(1-G)=2[1-(-5)]=12$ μF. For incremental capacitance the ideal DC source is shorted, so 7 μF and 3 μF are parallel, giving 10 μF. That is in series with 4 μF, giving $4(10)/(4+10)=20/7$ μF. The total seen at A is $12+20/7=14.857$ μF, or 14.86 μF.

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