Transient Analysis

Time-varying currents and voltages resulting from the abrupt change of the circuit (or due to switching) are called transients.

Important in many applications

Usually, transient analysis requires Ordinary Differential Equations to solve.

General Solutions

These general solutions can apply for both charging or discharging circuits.

Finding R

When you calculate , which is really , make sure to look at it from the capacitor/inductorβs perspective, not from like the sourceβs perspective.

R is the resistance as seen from the capacitor/inductorβs perspective. Review Theveninβs Theorem

General solution for capacitors (RC Circuits)

where

• = the final value or DC steady-state value when
• = the initial value
• = Time Constant

using the above formula for , DONβT use the follow below General solution for inductors (RL Circuits) where

• = the final value or DC steady-state value when
• = the initial value
• = Time Constant, where is the thevenin resistance as seen by the inductor

using the above formula for , DONβT use the formula of capacitor for voltage.

General Guidelines for solving these problems

Capacitors Capacitors act like open-circuit at , so current becomes 0 at infinity. You solve for voltage. β ALWAYS Treat conductor like open circuit to solve for voltage

Inductors In general, for inductors, to solve , the inductor will be short circuited as the circuit stabilizes.

Remember, an inductor acts like a short circuit in DC constant current. β AWAYS Treat inductor like short circuit and solve for current

Note on R_{th}

Just solve it the way you solve thevenin, easy.

Only exception is for finding the equivalent resistance, you treat sources and the inductor/capacitor as open-circuit as that is the definition of an equivalent/thevenin resistance.

β This got me quite confused.