Solved GATE Paper

GATE 2010 Electric Circuits Questions and Solutions

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

Question 1

In the circuit shown in the figure , the power supplied by the voltage source is:

GATE 2010 Electric Circuits Q1 circuit diagram
Circuit for GATE 2010 Electric Circuits Q1
  1. \(0\,W\)
  2. \(5\,W\)
  3. \(10\,W\)
  4. \(100\,W\)

Solution

  • Method: Apply Kirchhoff's Voltage Law (KVL) to the outer loop to find the current (\(I_1\)) supplied by the \(10\,V\) source.
  • Branch Currents: Let \(I_1\) be the current leaving the \(10\,V\) source. The two current sources fix the additional current carried by each arm of the outer loop, so the two \(2\,\Omega\) arms carry \(I_1 + 3\) and \(I_1 + 2\).
  • KVL on the Outer Loop:
    Equation
    \[2(I_1 + 3) + 2(I_1 + 2) = 10 \Rightarrow 4I_1 + 10 = 10 \Rightarrow I_1 = 0\,A\]
    The drops produced by the two current sources already account for the whole \(10\,V\), so the source itself carries no current.
  • Power Calculation: Power supplied by the voltage source is \(P = V \times I_1\).
    Equation
    \[P = 10\,V \times 0\,A = 0\,W\]
A
Final Answer
Correct answer: (1) \(0\,W\).
Question 02

Question 2

For the parallel RLC circuit, which one of the following statements is NOT correct?

  1. The bandwidth of the circuit decreases if \(R\) is increased
  2. The bandwidth of the circuit remains same if \(L\) is increased
  3. At resonance, input impedance is a real quantity
  4. At resonance, the magnitude of input impedance attains its minimum value

Solution

  • Formulas for Parallel RLC:
    • Bandwidth (BW): \(BW = \frac{1}{RC}\).
    • Input Impedance at resonance (\(Z_{in}\)): \(Z_{in} = R\).
  • Option 1 (True): If \(R\) increases, \(BW = 1/(RC)\) decreases.
  • Option 2 (True): \(BW = 1/(RC)\) does not depend on \(L\).
  • Option 3 (True): At resonance, the impedance is purely resistive (\(Z_{in}=R\)), which is a real quantity.
  • Option 4 (False): At resonance, the input impedance of a parallel RLC circuit is MAXIMUM (\(Z_{in}=R\)), not minimum. This statement is NOT correct.
D
Final Answer
Correct answer: (4) At resonance, the magnitude of input impedance attains its minimum value.
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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