Circuit Diagram Examples Using Kirchhoff's Rules

📚 Quick Study Guide

⚡
• Kirchhoff's Current Law (KCL): The total current entering a junction is equal to the total current leaving the junction. Mathematically, $\sum I_{in} = \sum I_{out}$.
🔋
• Kirchhoff's Voltage Law (KVL): The sum of the voltage drops in a closed loop is equal to the sum of the voltage sources in that loop. Mathematically, $\sum V_{sources} = \sum V_{drops}$.
💡
• Sign Conventions: When applying KVL, voltage drops are considered positive when traversing a resistor in the direction of the current, and voltage sources are positive when traversing from the negative to the positive terminal.
🧭
• Circuit Analysis Steps:
  ✏️
  1. Draw the circuit diagram and label all components.
  ➡️
  2. Assign current directions to each branch. If the assumed direction is wrong, the calculation will result in a negative current.
  ✅
  3. Apply KCL at junctions to reduce the number of unknowns.
  🔄
  4. Apply KVL to independent loops to obtain equations.
  ➕
  5. Solve the system of equations to find the unknown currents and voltages.

Practice Quiz

❓
1. What does Kirchhoff's Current Law (KCL) state?
   1. (A) The sum of voltages in a closed loop is zero.
   2. (B) The total current entering a junction equals the total current leaving the junction.
   3. (C) The voltage across a resistor is proportional to the current through it.
   4. (D) Energy is conserved in an electrical circuit.
❓
2. In Kirchhoff's Voltage Law (KVL), what is the sum of voltage drops and sources in a closed loop equal to?
   1. (A) Infinity
   2. (B) 1
   3. (C) 0
   4. (D) The total resistance in the loop
❓
3. When applying KVL, how is a voltage drop across a resistor typically treated when traversing in the direction of the current?
   1. (A) Negative
   2. (B) Positive
   3. (C) Zero
   4. (D) Ignored
❓
4. If the calculated current in a branch is negative after applying Kirchhoff's laws, what does this indicate?
   1. (A) There is a short circuit.
   2. (B) The assumed current direction was incorrect.
   3. (C) The voltage source is reversed.
   4. (D) The resistor value is too high.
❓
5. Consider a junction with three branches. If 2A enters the junction through one branch and 1A exits through another, what is the current in the third branch, and is it entering or exiting the junction?
   1. (A) 3A, entering
   2. (B) 1A, exiting
   3. (C) 1A, entering
   4. (D) 3A, exiting
❓
6. A loop contains a 12V source and two resistors. If the voltage drop across one resistor is 4V, what is the voltage drop across the other resistor?
   1. (A) 4V
   2. (B) 8V
   3. (C) 16V
   4. (D) 12V
❓
7. Which of the following is NOT a typical step in circuit analysis using Kirchhoff's Laws?
   1. (A) Drawing the circuit diagram and labeling components.
   2. (B) Assigning current directions to each branch.
   3. (C) Measuring the actual current with an ammeter before calculations.
   4. (D) Applying KCL at junctions to reduce unknowns.