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Chapter 3 Quiz — Kirchhoff's Laws and Circuit Topology

Test your understanding of Kirchhoff's Laws, circuit topology, and systematic analysis methods. Each question includes a detailed explanation.

Question 1

At a node, three currents enter: 2 A, 5 A, and 1 A. One current of 4 A leaves. What is the fifth current, and in which direction does it flow?

  1. 4 A, entering the node
  2. 4 A, leaving the node
  3. 8 A, leaving the node
  4. 8 A, entering the node
Show Answer

Correct Answer: B

By KCL: \(\sum I_{in} = \sum I_{out}\). Currents in: \(2 + 5 + 1 = 8\) A. Current out: 4 A. The fifth current must be \(8 - 4 = 4\) A leaving the node to balance.

Concept Tested: Kirchhoff's Current Law

Question 2

A loop contains a 15 V battery and three resistors. The voltage drops across the first two resistors are 6 V and 4 V. What is the voltage across the third resistor?

  1. 25 V
  2. 10 V
  3. 5 V
  4. 15 V
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Correct Answer: C

By KVL: \(V_s - V_{R1} - V_{R2} - V_{R3} = 0\). So \(15 - 6 - 4 - V_{R3} = 0\), giving \(V_{R3} = 5\) V.

Concept Tested: Kirchhoff's Voltage Law

Question 3

A circuit has 5 nodes and 8 branches. How many independent meshes does it have?

  1. 3
  2. 4
  3. 5
  4. 8
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Correct Answer: B

Using the topology formula: \(b = n - 1 + m\), so \(8 = 5 - 1 + m\), giving \(m = 4\) independent meshes.

Concept Tested: Circuit Topology

Question 4

When should you use a supernode in the node voltage method?

  1. When a current source connects two non-reference nodes
  2. When a voltage source connects two non-reference nodes
  3. When a resistor connects to ground
  4. When the circuit has more than three nodes
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Correct Answer: B

A supernode is needed when a voltage source connects two non-reference nodes. The current through an ideal voltage source is unknown, so standard KCL cannot be applied. The supernode encloses both nodes and adds a constraint equation from the source voltage.

Concept Tested: Supernode Technique

Question 5

To apply superposition in a circuit with two voltage sources, what do you do to each source when analyzing the other?

  1. Remove the source entirely
  2. Replace it with an open circuit
  3. Replace it with a short circuit
  4. Replace it with a 1 Ω resistor
Show Answer

Correct Answer: C

When deactivating a voltage source for superposition, replace it with a short circuit (0 V, wire). Current sources are replaced with open circuits (0 A, break). This preserves the circuit connections while removing the source's contribution.

Concept Tested: Superposition Principle

Question 6

What is the difference between a loop and a mesh?

  1. A loop must be clockwise; a mesh can be either direction
  2. A mesh is a loop that contains no other loops inside it
  3. A loop is always planar; a mesh may be non-planar
  4. There is no difference — the terms are interchangeable
Show Answer

Correct Answer: B

A loop is any closed path through a circuit. A mesh is a special case — a loop that contains no other loops within it (a minimal loop). Every mesh is a loop, but not every loop is a mesh.

Concept Tested: Circuit Topology

Answers Summary

Question Answer Concept Tested
1 B Kirchhoff's Current Law
2 C Kirchhoff's Voltage Law
3 B Circuit Topology
4 B Supernode Technique
5 C Superposition Principle
6 B Circuit Topology