EE301 – INDUCTOR TRANSIENT ANALYSIS
1 9/19/2016
L
vE
Learning Objectives
a. Calculate inductor voltage and current as a function of time
b. Explain inductor DC characteristics
c. Calculate inductor energy stored
Inductance and Steady State DC Recall that in steady state DC, an
inductor looks like a short circuit. Stated another way, in steady state DC,
the induced voltage across an inductor is equal to zero volts.
But what happens when we are not in steady state? Suppose we have the
circuit shown below, in which the switch is initially open. Suppose
someone in downtown Annapolis was threatening to beat you up unless
you could tell them what happens when the switch is shut?
Since the safety and well-being of midshipmen is our primary
concern, today we cover inductor transient analysis, so you will be
safe next time you run into a gang of thugs in downtown Annapolis.
Transient Analysis: Inductor Storage Phase In the circuit above,
when the switch is open, the inductor acts as a short circuit. But since
the battery is not connected, no current flows anywhere.
When switch is closed, the current through the branch with the
inductor immediately “wants to change.” The current through an inductor cannot change instantaneously
(although the voltage across it can). In an attempt to keep the current through it from changing, the
inductor immediately induces a voltage that opposes that change, which keeps the current near zero:
As the current L
istarts to build up, the voltage across the R1 resistor increases. As the voltage across R1
increases, the voltage drop across the inductor will decrease (since, by KVL) the voltage across R1 plus
the voltage across the inductor must sum to the fixed battery voltage, E.
Inductor Storage Phase Equations The voltages and currents in the circuit above change
exponentially over time, according to the equations shown below:
