Kirchhoff's Voltage Law (KVL) Explained: Proof with Inductor Circuit

To prove Kirchhoff's voltage law (KVL) in the example you referred to, let's consider a simple circuit with two inductors connected in series through a switch. Initially, the switch is closed, allowing each inductor to carry an arbitrary current, denoted by I1 and I2. Then, the switch opens.

To apply KVL, we need to consider the voltage drops and rises around a closed loop. In this case, we can choose the loop that includes both inductors.

Considering the loop, let's examine the voltage drops and rises across the elements:

1. Voltage drop across inductor 1 (V1):

   • Since the current in inductor 1 is decreasing due to the switch opening, there will be a voltage drop across it. Let's denote it as V1.

2. Voltage drop across inductor 2 (V2):

   • Similarly, as the current in inductor 2 is decreasing, there will be a voltage drop across it. Let's denote it as V2.

According to KVL, the sum of the voltage drops and rises around the loop must be zero:

V1 + V2 = 0

Therefore, we can conclude that KVL holds true in this circuit.

This result shows that the voltage drop across inductor 1 (V1) is equal in magnitude and opposite in polarity to the voltage drop across inductor 2 (V2), resulting in the sum of these voltage drops being zero.