Ohm's Law is not directly applicable to determining the current through an inductor in a transient response. Ohm's Law is a fundamental principle in electrical circuits that relates voltage (V), current (I), and resistance (R) and is expressed as:
V = I * R
However, inductors behave differently than resistors in transient responses. When there is a change in voltage across an inductor, it induces an opposing electromotive force (EMF) that opposes the change. This phenomenon is described by Faraday's law of electromagnetic induction. The equation for the induced EMF (e) in an inductor is:
e = -L * di/dt
Where:
e is the induced electromotive force (EMF) in volts (V).
L is the inductance of the inductor in henries (H).
di/dt is the rate of change of current (I) with respect to time (t) in amperes per second (A/s).
Now, let's see how Ohm's Law can be applied in combination with the above equation to determine the current through an inductor in a transient response.
Consider a simple RL (resistor-inductor) circuit in which an inductor is connected in series with a resistor and a voltage source (for example, a step input). When the voltage is suddenly applied or changed, the inductor resists the change in current through the induced EMF.
The total voltage across the circuit is the sum of the voltage across the resistor (V_R) and the voltage across the inductor (V_L):
V_total = V_R + V_L
Using Ohm's Law for the resistor (V_R = I * R) and the equation for the voltage across the inductor (V_L = L * di/dt), we get:
V_total = I * R + L * di/dt
Now, let's say we know the values of R (resistance), L (inductance), and V_total (applied voltage). To determine the current (I) through the inductor at a particular time (t), you would need to solve the above equation for I.
The process of solving this type of differential equation is called "transient analysis," and it provides insights into how the current through the inductor changes over time in response to the applied voltage.
In summary, Ohm's Law is not directly applied to inductors in transient responses. Instead, it is combined with Faraday's law of electromagnetic induction to analyze the behavior of inductors in time-varying circuits. This analysis helps determine the current through the inductor as the circuit reaches a stable state after a sudden change in voltage.