1. Lesson 13: Inductor Transient Analysis

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

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

4. Inductor Charging Equations
As current (iL) across the inductor builds up, the voltage across the R1 resistor increases.
Voltages and currents in a the inductor charging circuit change exponentially over time.

5. Power/Energy
Similarly to capacitance; the energy stored in an inductor can be calculated by:

6. Steady State Conditions
When the circuit is at steady state:
The 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 spikes in thousands of volts range.

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
Assume an Inductor is initially fully charged with a constant 100 mA (IO) current flow. It acts like a short circuit…
When the 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 discharge equation for the VL, iL,. -

16. QUESTIONS?