1. Lesson 12 Inductors Transient Analysis

2. Learning Objectives
Calculate inductor voltage and current as a function of time.
Explain inductor DC characteristics.

3. Inductor Charging Inductor: Oppose Changes (Choking effects)
Inductor is initially fully discharged
acts like a open circuit
When switch is closed, the changing current across the inductor immediately induces a voltage that opposes that change, which keeps the current near zero:

4. Inductor charging
As current iL builds up, the voltage across the R1 resistor increases.

5. Inductor Charging Equations
Voltages and currents in a charging circuit change exponentially over time

6. Steady State Conditions
Circuit is at steady state: voltage and current reach their final values and stop changing
There is no change in current in the circuit, so the inductor has zero voltage induced across it. Inductor current will be steady:
Inductor then looks like a short circuit

7. The Time Constant
Rate at which an inductor charges depends on R and L, which is called the TIME CONSTANT:
Transients can be considered to last for five time constants

8. Example Problem 1
In the circuit below, the switch is initially open and conditions are at steady-state.
After the switch is shut, determine:
how long it will take for the inductor to reach a steady-state condition (>99% of final current).
Write the equation for the VL(t) & iL(t). Sketch the transient.
Find the Energy stored in the Inductor.

9. Interrupting Current in an Inductive Circuit
When switch opens in an RL circuit
Energy is released in a short time
This may create a large voltage
Induced voltage is called an inductive kick
Opening of inductive circuit may cause voltage sparks of thousands of volts

10. Interrupting a Circuit
Switch flashovers are generally undesirable
They can be controlled with proper engineering design
These large voltages can be useful
Such as in automotive ignition systems

11. Inductor Discharging
Inductor is initially fully charged with constant 100 ma current through it. It acts like a short circuit
When switch is opened, the inductor will immediately induce a voltage to keep the 100 mA current constant.
KVL can be used to calculate this induced voltage
Notice the polarity of the induced voltage!

12. Inductor Discharging
As stored energy is released, the induced voltage across the inductor drops.
This makes the voltage drop across the resistor drop, so current in the circuit drops

13. Inductor Discharging Equations
Voltages and currents in a discharging circuit also change exponentially over time

14. The Time Constant
Rate at which an inductor discharges depends on R and L, which is called the TIME CONSTANT:
Transients can be considered to last for five time constants

15. Example Problem 2
The circuit shown below has been in operation with the switch shut for a long time. The switch opens at time t = 0, determine:
how long it will take for the inductor to discharge.
Write the equation for the VL, iL,. Sketch the transient.