Kirchhoff’s Laws- Current and Electricity - Kirchhoff Voltage Rule

• Introduced by Gustav Kirchhoff in 1845
• Used to analyze complex electrical circuits

Kirchhoff’s Laws

1. Kirchhoff’s Current Law (KCL):
   • The algebraic sum of currents at any junction in a circuit is zero
   • Conservation of charge

2. Kirchhoff’s Voltage Law (KVL):
   • The algebraic sum of voltage drops (IR drops) and rises (EMF) in any closed loop is zero
   • Conservation of energy

Kirchhoff Voltage Rule

• Also known as Kirchhoff’s Second Law or KVL
• States that the total sum of voltages around any closed loop in a circuit is zero
• Considering polarity conventions and sign conventions for voltage drops and rises

Using Kirchhoff Voltage Rule

Steps to apply Kirchhoff Voltage Rule:

1. Assign polarities to each resistor and EMF source in the circuit.

2. Choose a direction for the loop and assign a sign convention (+/-) for the voltage drops and rises.

3. Apply the Kirchhoff Voltage Rule to write the algebraic sum of voltages around the loop.

4. Solve the resulting equations to determine the unknown currents or voltages in the circuit.

Example Circuit

• Let’s consider a simple circuit with two resistors and a battery
• Resistance of the first resistor: R1
• Resistance of the second resistor: R2
• EMF of the battery: E `` +- R1 -+ | |
  • | | - | E | | R2
  • | | - | | +-+ ``

Applying Kirchhoff Voltage Rule

1. Assign polarities:
   • Positive terminal of the battery: Higher potential
   • Negative terminal of the battery: Lower potential
   • Direction of current flow: Clockwise

2. Choose the loop direction and sign convention:
   • Loop direction: Clockwise
   • Voltage drop across R1: +IR1
   • Voltage drop across R2: +IR2
   • EMF of the battery: -E

3. Apply the Kirchhoff Voltage Rule: +IR1 + IR2 - E = 0

4. Solve the equation to find the currents or voltages in the circuit.

11. Example Calculation

• Let’s consider the values for the circuit:

  • R1 = 20 Ω
  • R2 = 10 Ω
  • E = 12 V

• Applying the Kirchhoff Voltage Rule: +I(20) + I(10) - 12 = 0

• Simplifying the equation: 20I + 10I - 12 = 0 30I = 12 I = 0.4 A

12. Find Voltage Drop across Each Resistor

• Using Ohm’s Law, we can find the voltage drop across each resistor:
  • Voltage drop across R1: V1 = IR1 V1 = (0.4 A)(20 Ω) V1 = 8 V
  • Voltage drop across R2: V2 = IR2 V2 = (0.4 A)(10 Ω) V2 = 4 V

13. Applying Kirchhoff Voltage Rule in Complex Circuits

• Kirchhoff Voltage Rule is applicable to more complex circuits as well
• It can be used to solve circuits with multiple loops and branches
• The same principles of assigning polarities and sign conventions apply

14. Example Circuit with Multiple Loops

• Let’s consider a circuit with two loops and three resistors: + R1 --+ | | --++ ++ | | | | --++--++-- | | + R2 --+ | | R3

15. Applying Kirchhoff Voltage Rule for Loop 1

• Assigning polarities and direction for Loop 1:
  • Polarities: Assign positive and negative terminals to each resistor
  • Direction: Clockwise

16. Applying Kirchhoff Voltage Rule for Loop 1

• Using sign conventions for Loop 1:
  • Voltage drop across R1 (positive terminal to negative terminal): +IR1
  • Voltage drop across R2 (positive terminal to negative terminal): -IR2

17. Applying Kirchhoff Voltage Rule for Loop 1

• Applying Kirchhoff Voltage Rule for Loop 1: +IR1 - IR2 = 0

18. Applying Kirchhoff Voltage Rule for Loop 2

• Assigning polarities and direction for Loop 2:
  • Polarities: Assign positive and negative terminals to each resistor
  • Direction: Counterclockwise

19. Applying Kirchhoff Voltage Rule for Loop 2

• Using sign conventions for Loop 2:
  • Voltage drop across R2 (positive terminal to negative terminal): +IR2
  • Voltage drop across R3 (positive terminal to negative terminal): -IR3

20. Applying Kirchhoff Voltage Rule for Loop 2

• Applying Kirchhoff Voltage Rule for Loop 2: +IR2 - IR3 = 0

21. Example Calculation - Loop 1

• Let’s consider the values for the circuit:
  • R1 = 10 Ω
  • R2 = 15 Ω
• Applying the Kirchhoff Voltage Rule for Loop 1: 10I - 15I = 0 -5I = 0 I = 0 A

22. Example Calculation - Loop 2

• Let’s consider the values for the circuit:
  • R2 = 15 Ω
  • R3 = 25 Ω
• Applying the Kirchhoff Voltage Rule for Loop 2: 15I - 25I = 0 -10I = 0 I = 0 A

23. Limitations of Kirchhoff’s Laws

• Kirchhoff’s Laws are based on certain assumptions and have limitations:
  1. Resistors should follow Ohm’s Law.
  2. The circuit should be in a steady state.
  3. Kirchhoff’s Laws do not consider magnetic fields and inductive effects.

24. Applications of Kirchhoff’s Laws

• Kirchhoff’s Laws find wide applications in various areas:
  1. Electrical networks and circuit analysis.
  2. Design and analysis of electronic circuits.
  3. Power distribution systems.
  4. Control systems and feedback circuits.

25. Example: Wheatstone Bridge

• The Wheatstone Bridge is a type of circuit used to measure unknown resistances.
• It consists of four resistors connected in a diamond shape.

26. Wheatstone Bridge Operation

• A voltage source is connected across one diagonal of the bridge, and a galvanometer is connected across the other diagonal.
• By adjusting one resistor, the bridge can be balanced, indicating that the ratio of the other resistors is equal to the unknown resistance.

27. Example: Bridge Circuit Calculation

• Let’s consider a Wheatstone bridge circuit: R1 -+++- | | | | R | | | | -+++- R2 R3
• If R1 = 30 Ω, R2 = 20 Ω, and R3 = 40 Ω, what is the value of R?

28. Wheatstone Bridge Calculation

• Using the balance condition of the bridge: R1/R2 = R/R3

• Substituting the given values: 30/20 = R/40

• Solving the equation: 30 * 40 = 20R R = 60 Ω

29. Summary

• Kirchhoff’s Laws are fundamental principles used to analyze electrical circuits.
• Kirchhoff’s Current Law deals with the conservation of charge in a circuit.
• Kirchhoff’s Voltage Law deals with the conservation of energy in a circuit.
• Kirchhoff’s Laws are useful in solving complex circuits and finding unknown currents or voltages.
• They have applications in circuit analysis, design, and various electrical systems.

30. Conclusion

• Kirchhoff’s Laws provide a powerful tool for analyzing electrical circuits, enabling us to determine the currents and voltages in a system accurately. By applying Kirchhoff’s Laws and understanding their principles, we can solve complex circuits and design efficient electrical systems. These laws have numerous applications in various fields of electronics and electrical engineering, making them an essential concept to master for 12th Boards Physics students. Practice and application of Kirchhoff’s Laws will further enhance your problem-solving skills and understanding of electrical circuits.