Circuit Diagram Examples Using Kirchhoff's Laws

📚 Kirchhoff's Laws Quick Study Guide

• ⚡ Kirchhoff's Current Law (KCL): The total current entering a junction is equal to the total current leaving the junction. Mathematically, $\sum I_{in} = \sum I_{out}$. This law is based on the conservation of charge.
• 💡 Kirchhoff's Voltage Law (KVL): The sum of all voltage drops around any closed loop in a circuit is equal to zero. Mathematically, $\sum V = 0$. This law is based on the conservation of energy.
• 📏 Sign Conventions: When applying KVL, voltage drops are usually considered positive, and voltage rises are considered negative (or vice versa, as long as you are consistent).
• 🔍 Series Resistors: The equivalent resistance of resistors in series is the sum of individual resistances: $R_{eq} = R_1 + R_2 + R_3 + ...$
• ⎔ Parallel Resistors: The reciprocal of the equivalent resistance of resistors in parallel is the sum of the reciprocals of individual resistances: $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ...$
• 📝 Steps to Solve Circuit Problems:
  1. Draw the circuit diagram.
  2. Assign current directions and label voltages.
  3. Apply KCL at junctions.
  4. Apply KVL to loops.
  5. Solve the resulting system of equations.

🧪 Practice Quiz

1. Question 1: According to Kirchhoff's Current Law (KCL), what is the sum of currents entering and leaving a node in a circuit?
   1. A. Infinity
   2. B. Equal to the voltage source
   3. C. Zero
   4. D. Equal to the highest resistance in the circuit
2. Question 2: What principle is Kirchhoff's Voltage Law (KVL) based on?
   1. A. Conservation of Charge
   2. B. Conservation of Momentum
   3. C. Conservation of Energy
   4. D. Ohm's Law
3. Question 3: In a series circuit with two resistors, $R_1 = 10 \Omega$ and $R_2 = 20 \Omega$, what is the equivalent resistance?
   1. A. $10 \Omega$
   2. B. $20 \Omega$
   3. C. $30 \Omega$
   4. D. $2/3 \Omega$
4. Question 4: In a parallel circuit with two resistors, $R_1 = 4 \Omega$ and $R_2 = 4 \Omega$, what is the equivalent resistance?
   1. A. $8 \Omega$
   2. B. $0.25 \Omega$
   3. C. $2 \Omega$
   4. D. $4 \Omega$
5. Question 5: If the voltage drop across a resistor is 5V and the current through it is 2A, what is the resistance?
   1. A. 2.5 $\Omega$
   2. B. 10 $\Omega$
   3. C. 7 $\Omega$
   4. D. 0.4 $\Omega$
6. Question 6: In a closed loop, if there are two voltage sources, one 10V and the other -5V, what must the sum of the voltage drops across other components be to satisfy KVL?
   1. A. -15V
   2. B. 5V
   3. C. -5V
   4. D. 15V
7. Question 7: What is the first step in solving a complex circuit using Kirchhoff's Laws?
   1. A. Solve the equations
   2. B. Apply KVL to loops
   3. C. Draw the circuit diagram
   4. D. Assign resistance values