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GATE 2021 EE – Question 40

Electric Circuits · Network Elements: Ideal voltage and current sources, dependent sources, R, L, C, M elements · 2 marks · Multiple choice

The input impedance, $Z_{in}(s)$, for the network shown is

Diagram for GATE 2021 EE question 40
  1. $\dfrac{23s^2+46s+20}{4s+5}$
  2. $6s+4$
  3. $7s+4$
  4. $\dfrac{25s^2+46s+20}{4s+5}$

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Show answer and explanation

Correct answer: (A) $\dfrac{23s^2+46s+20}{4s+5}$

Explanation

With the secondary closed by $5\ \Omega$, $Z_{in}=4+6s-\frac{(sM)^2}{4s+5}$ for $M=1$ H (the mutual term is subtracted for this winding arrangement). Then $Z_{in}=\frac{(4+6s)(4s+5)-s^2}{4s+5}=\frac{23s^2+46s+20}{4s+5}$.