Post 3: Kirchhoff's Second Law (KVL) – The Law of Conservation of Energy

Kirchhoff's Second Law, also known as the Law of Conservation of Energy or Kirchhoff's Voltage Law (KVL), is essential in understanding the behavior of electrical circuits. It states that the sum of the voltage drops across all the elements in a closed loop is equal to the applied electromotive force (EMF) or voltage.

KVL is based on the principle of energy conservation, indicating that the total energy supplied by a source is equal to the total energy consumed by the circuit components. By applying KVL, we can determine the voltage drops across circuit elements and analyze their behavior in a closed loop.

Formula: According to Kirchhoff's Voltage Law (KVL), the sum of the voltage drops around a closed loop is equal to the sum of the voltage sources in that loop:

Σ(Voltage Drops) = Σ(Voltage Sources)

This equation can be expressed as: Σ(Voltage Drops) - Σ(Voltage Sources) = 0

Example:

Let's consider the following circuit:

     +----R1----+
     |           |
   EMF           R2
     |           |
     +----R3----+

In this circuit, there are three resistors (R1, R2, and R3) and an EMF source. We will use KVL to determine the voltage drops across each resistor.

Step 1: Assign direction and label voltages: Assign a direction for the current flow in the loop. Label the voltage drops across each resistor and the EMF source.

     +---R1---+
     |        |
   EMF        R2
     |        |
     +---R3---+

Step 2: Set up the KVL equation: According to KVL, the sum of the voltage drops across all elements in a closed loop should be equal to the sum of the voltage sources, which, in this case, is the EMF.

Voltage drop across R1 + Voltage drop across R2 + Voltage drop across R3 = EMF

Step 3: Apply Ohm's Law to find the voltage drops: Using Ohm's Law (V = I * R) for each resistor, we can express the voltage drops in terms of the current flowing through the circuit.

Voltage drop across R1: V1 = I * R1 Voltage drop across R2: V2 = I * R2 Voltage drop across R3: V3 = I * R3

Step 4: Substituting and simplifying: Substitute the expressions for the voltage drops into the KVL equation and simplify.

(I * R1) + (I * R2) + (I * R3) = EMF I * (R1 + R2 + R3) = EMF

Simplifying further, we get:

I = EMF / (R1 + R2 + R3)

Step 5: Solve for the voltage drops: Now that we have the current flowing through the circuit, we can substitute it back into the expressions for the voltage drops:

Voltage drop across R1: V1 = I * R1 Voltage drop across R2: V2 = I * R2 Voltage drop across R3: V3 = I * R3

By substituting the value of I, we can calculate the voltage drops across each resistor.

Conclusion: Kirchhoff's Second Law, the Law of Conservation of Energy (KVL), allows us to analyze and solve complex circuits by understanding the behavior of voltage drops across elements in a closed loop. By applying KVL, we can determine the voltage drops across resistors and other components, aiding in circuit analysis and design.