Kirchhoff's Voltage Law (KVL)

Overview of KVL

• Kirchhoff's Voltage Law states that in a closed circuit, the sum of all voltages must equal zero.
• Voltages can be positive or negative based on the direction of current flow.

Understanding Voltage and Current Flow

• Resistor Example:

  • Current flows from higher potential (20V) to lower potential (10V).
  • Resistor consumes energy, hence assigned a negative voltage.
  • Voltage is defined as energy change per unit charge (1 Volt = 1 Joule/Coulomb).

• Battery Example:

  • Current can flow from low potential (0V) to high potential (12V).
  • Battery increases energy of charges, hence assigned a positive voltage.

Assigning Voltage Values

• Resistor:
  • Always results in a negative voltage drop because it consumes energy.
• Battery:
  • If current flows from low to high potential, it contributes a positive voltage (increases energy).
  • If current flows from high to low potential, it contributes a negative voltage (decreases energy).

Kirchhoff's Voltage Law Application in Circuits

1. Practice Problem Setup:

   • Battery (12V) connected to resistors (8Ω, 10Ω, 12Ω).
   • Define voltages in the circuit according to KVL.
   • Current flows from battery's positive terminal through resistors.

2. Equation Formation:

   [ V_{b} - V_{1} - V_{2} - V_{3} = 0 ]

   • Where
   • ( V_{b} = 12V )
   • ( V_{1} = IR_{1} ) (Resistor voltage drop)
   • Continue similar for other resistors.

3. Calculating Current:

   • Using Ohm's Law:
   • ( V = IR )
   • Substitute resistances and solve for current.
   • Example: ( I = \frac{12V}{30Ω} = 0.4 A )_

Potential Calculation in Circuit

• Calculate potentials at various points:
  • Point A (12V): Battery positive side
  • Point B: Voltage drop across Resistor R1 (8Ω):
    ( V_{B} = 12V - (I \times R1) = 8.8V )
  • Point C: Continue this for other resistors using similar equations._

Example with Multiple Components

1. Circuit Setup:

   • Battery (50V), resistors (30Ω, 70Ω), and additional batteries (10V, 20V).
   • Determine current direction based on battery voltages.

2. Voltage Equation Setup:

   • Set up voltage equation considering all batteries and resistors.
   • Combine terms and solve for current.

3. Calculating Potentials:

   • Follow similar steps as before to find potentials at each point in the circuit.
   • Example:
   • Assign potentials starting from the battery and accounting for drops across resistors.

Key Takeaways

• Resistors always lead to negative voltage due to energy consumption.
• Batteries can either increase (positive voltage) or decrease (negative voltage) energy based on current direction.
• KVL is essential for analyzing complex circuits and determining current and voltage drops.