Understanding Kirchhoff's Voltage Law (KVL) with Inductor Circuits

This tutorial demonstrates how Kirchhoff's Voltage Law (KVL) applies to circuits containing inductors. We'll use the formula relating voltage across an inductor to the rate of change of current:

V = L * di/dt

where:

V is the voltage across the inductor * L is the inductance of the inductor* di/dt represents the rate of change of current

Let's analyze a circuit with two inductors connected in a loop. Applying KVL to this loop gives us:

V1 + V2 = 0

Now, let's substitute the voltage drops across each inductor using the formula:

V1 = L1 * di1/dt* V2 = L2 * di2/dt

Plugging these into the KVL equation:

L1 * di1/dt + L2 * di2/dt = 0

Rearranging and factoring out 'dt':

(di1 + di2) / dt = 0

Since 'dt' cannot be zero, the sum of the differentials (di1 + di2) must always equal zero. This means:

di1 + di2 = 0

Therefore, the rate of change of current in inductor 1 (-di1/dt) has the same magnitude but opposite sign as the rate of change of current in inductor 2 (di2/dt).

This example demonstrates how applying KVL with the formula for voltage across an inductor confirms that the total voltage drops around a loop sum to zero, validating Kirchhoff's Voltage Law in inductive circuits.

Understanding Kirchhoff's Voltage Law (KVL) with Inductor Circuits