Lect14EEE 2021 Analysis Methods for Transient Circuits Dr. Holbert March 17, 2008

Lect14EEE 2022 Impedance, Z Using Ohm’s Law, impedance (Z) can be defined via: V = I Z Circuit Element Impedance (ohms) ResistorR Capacitor1 / (sC) InductorsL

Lect14EEE 2023 LC Behavior Recall some facts on the behavior of LC elements Inductors (L): –The current in an inductor cannot change abruptly in zero time; an inductor makes itself felt in a circuit only when there is a changing current –An inductor looks like a short circuit to d.c. Capacitors (C): –The voltage across a capacitor cannot change discontinuously; a capacitor makes itself felt only when there exists a changing potential (voltage) difference –A capacitor looks like an open circuit to d.c.

Lect14EEE 2024 Step-by-Step Approach 1.Assume solution (only dc sources allowed): x(t) = K 1 + K 2 e -t/  2.At t=0 –, draw the circuit with C as open circuit or L as short circuit; find V C (0 – ) or I L (0 – ) 3.At t=0 +, redraw circuit and replace C or L with appropriate source of value obtained in step #2, and find x(0)=K 1 +K 2 4.At t= , repeat step #2 to find x(  )=K 1

Lect14EEE 2025 Step-by-Step Approach (cont’d) 5.Find time constant (  ) Looking across the terminals of the C or L element, form Thevenin equivalent circuit;  =R Th C or  =L/R Th 6.Finish up Simply put the answer together This is essentially the inspection method except it is expressed in a systematic procedure

Lect14EEE 2026 Class Examples Drill Problems P6-6, P6-7, P6-8, P6-13, P6-14 –We’ll use the inspection (step-by-step) approach for P6-7 and P6-8