Solved GATE Paper

GATE 2007 Electric Circuits Questions and Solutions

Instructor: Prof. Mithun Mondal Institution: BITS Pilani Subject: Electric Circuits
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Question 01

Question 1

For the circuit shown in the figure , the Thevenin voltage and resistance looking into X-Y are:

GATE 2007 Electric Circuits Q1 circuit diagram
Circuit for GATE 2007 Electric Circuits Q1
  1. \(\frac{4}{3}V\), \(2\,\Omega\)
  2. \(4V\), \(\frac{2}{3}\,\Omega\)
  3. \(\frac{4}{3}V\), \(\frac{2}{3}\,\Omega\)
  4. \(4V\), \(2\,\Omega\)

Solution

  • Thevenin Voltage (\(V_{Th}\)): By applying KCL at the output node \(V_X\), we find \(V_{Th} = 4\,V\).
  • Thevenin Resistance (\(R_{Th}\)): By calculating the short-circuit current (\(I_{SC} = 2\,A\)), we get \(R_{Th} = V_{Th}/I_{SC} = 4/2 = 2\,\Omega\).
D
Final Answer
Correct answer: (4) \(4V\), \(2\,\Omega\).
Question 02

Question 2

The RC circuit shown in the figure is:

GATE 2007 Electric Circuits Q2 circuit diagram
Circuit for GATE 2007 Electric Circuits Q2
  1. A low-pass filter
  2. A high-pass filter
  3. A band-pass filter
  4. A band-reject filter

Solution

  • At \(\omega \to 0\): The series capacitor is an open circuit, resulting in zero gain.
  • At \(\omega \to \infty\): The parallel capacitor is a short circuit, resulting in zero gain.
  • Since the circuit blocks both extremes but passes intermediate frequencies, it is a band-pass filter.
C
Final Answer
Correct answer: (3) A band-pass filter.
Question 03

Question 3

The condition for maximum power transfer to a load impedance \(Z_L = R_L + jX_L\) from a source with internal impedance \(Z_S = R_S + jX_S\) is:

  1. \(R_L = R_S\) and \(X_L = X_S\)
  2. \(R_L = R_S\) and \(X_L = -X_S\)
  3. \(R_L = |Z_S|\) and \(X_L = 0\)
  4. \(Z_L = R_S\)

Solution

  • For a complex source impedance, maximum power is transferred when the load impedance is the conjugate of the source impedance, i.e., \(Z_L = Z_S^*\).
B
Final Answer
Correct answer: (2) \(R_L = R_S\) and \(X_L = -X_S\).
Question 04

Question 4

A two-port network is reciprocal if its admittance parameters satisfy which of the following conditions?

  1. \(y_{11} = y_{22}\)
  2. \(y_{12} = -y_{21}\)
  3. \(y_{12} = y_{21}\)
  4. \(y_{11}y_{22} - y_{12}y_{21} = 1\)

Solution

  • A two-port network is considered reciprocal if the ratio of the output current (Port 2) to the input voltage (Port 1) equals the ratio of the input current (Port 1) to the output voltage (Port 2) under appropriate open/short circuit conditions. In terms of the Y-parameters (Admittance parameters), this condition is \(y_{12} = y_{21}\).
  • The condition \(y_{11} = y_{22}\) indicates a symmetric network.
C
Final Answer
Correct answer: (3) \(y_{12} = y_{21}\).
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