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Chapter 4 Quiz — DC Circuit Analysis Methods

Multiple Choice Questions

1. A 20 V voltage source in series with a 5 Ω resistor is transformed to its Norton equivalent. What is the Norton current?

  • A) 4 A
  • B) 100 A
  • C) 0.25 A
  • D) 5 A
Answer

A) 4 A

Norton current \(I_N = V_S / R_S = 20 / 5 = 4\) A. The Norton equivalent consists of a 4 A current source in parallel with a 5 Ω resistor.

2. To find the Thévenin resistance \(R_{Th}\) of a circuit containing only independent sources, you:

  • A) Calculate \(V_{oc} / V_S\)
  • B) Kill all independent sources and find the resistance looking into the terminals
  • C) Short all terminals and measure current
  • D) Add all resistances in the circuit
Answer

B) Kill all independent sources and find the resistance looking into the terminals

Independent voltage sources are replaced by short circuits and independent current sources are replaced by open circuits. Then the resistance seen at the terminals is \(R_{Th}\).

3. A circuit's Thévenin equivalent has \(V_{Th} = 12\) V and \(R_{Th} = 4\) Ω. What value of load resistance \(R_L\) maximizes power transfer to the load?

  • A) 2 Ω
  • B) 8 Ω
  • C) 4 Ω
  • D) 12 Ω
Answer

C) 4 Ω

By the maximum power transfer theorem, \(R_L = R_{Th} = 4\) Ω for maximum power.

4. Using the circuit in Q3 with \(R_L = R_{Th} = 4\) Ω, what is the maximum power delivered to the load?

  • A) 9 W
  • B) 36 W
  • C) 18 W
  • D) 3 W
Answer

A) 9 W

\(P_{max} = V_{Th}^2 / (4 R_{Th}) = 144 / (4 \times 4) = 144 / 16 = 9\) W.

5. A Thévenin equivalent has \(V_{Th} = 8\) V and \(R_{Th} = 2\) Ω. What is the Norton equivalent current source?

  • A) 16 A
  • B) 0.25 A
  • C) 4 A
  • D) 2 A
Answer

C) 4 A

\(I_N = V_{Th} / R_{Th} = 8 / 2 = 4\) A. The Norton resistance \(R_N = R_{Th} = 2\) Ω.

6. When finding the Thévenin resistance of a circuit containing dependent sources, you should:

  • A) Kill all sources including dependent ones
  • B) Kill only independent sources and apply a test voltage or current at the terminals
  • C) Short all terminals and measure voltage
  • D) Only kill voltage sources, leave current sources active
Answer

B) Kill only independent sources and apply a test voltage or current at the terminals

Dependent sources must remain active. Apply a test voltage \(V_T\) or current \(I_T\) to the terminals, then \(R_{Th} = V_T / I_T\).

7. The efficiency at maximum power transfer (when \(R_L = R_{Th}\)) is:

  • A) 100%
  • B) 75%
  • C) 25%
  • D) 50%
Answer

D) 50%

When \(R_L = R_{Th}\), equal power is dissipated in the load and in the source resistance, so the efficiency is exactly 50%.

8. A source has output resistance \(R_{out} = 500\) Ω and open-circuit voltage of 5 V. It drives a load with input resistance \(R_{in} = 500\) Ω. What voltage appears across the load?

  • A) 5 V
  • B) 1 V
  • C) 2.5 V
  • D) 0 V
Answer

C) 2.5 V

Loading effect: \(V_{load} = V_S \times R_{in}/(R_{out} + R_{in}) = 5 \times 500/1000 = 2.5\) V. The 500 Ω source resistance and 500 Ω load form a voltage divider.

9. Which of the following is NOT a valid two-port network parameter set?

  • A) Z-parameters
  • B) h-parameters
  • C) R-parameters
  • D) Y-parameters
Answer

C) R-parameters

Standard two-port parameter sets include Z (impedance), Y (admittance), h (hybrid), g (inverse hybrid), and ABCD (transmission) parameters. There is no "R-parameter" set.

10. A current source of 6 A in parallel with a 3 Ω resistor is converted to its Thévenin equivalent. What is \(V_{Th}\)?

  • A) 2 V
  • B) 0.5 V
  • C) 18 V
  • D) 3 V
Answer

C) 18 V

\(V_{Th} = I_N \times R_P = 6 \times 3 = 18\) V. The Thévenin equivalent is an 18 V source in series with a 3 Ω resistor.