The Laws of Circuit - you can learn and practice by just reading

Copyright. Charles Kim 2006

Why Transient Analysis?
Then why are we interested in the transient (or transition) period after switching? It's because there are a lot of such demands in real world. Think about a defibrillator which applies shock voltage (or current) to unbeating heart. You need very high level energy but at the same time you do not want to apply that high level of energy for a long time. You do only a few milliseconds. Of course after that period, your energy level must be zero. Now we are interested in the level of energy and the time period in terms of circuit analysis. Then what is t<0 event in the defibilitator example? During t<0 , it is charging a capacitor. For t>0 analysis, the voltage source is removed by a switching action at t=0 (remember that they press the switch in ER), but the charged energy in the capacitor will flow through the heart until it is fully discharged. Since there is no source connected in the circuit, after the discharge, there is no voltage applied to the heart.
Another example. Ignition in automobile. To start your car, you turn your ignition switch, then your hear the beautiful sound of starter motor then the gasoline engine picks up. Optimum starting operation requires, for example, a current reaching at least 1 A within 100ms and remains above 1A for 1 - 1.5s. So how do you design your ignition circuit? Simply put, R(modeled from ignition coil resistance), C, and L (modeled from the ignition coil) and the 12V battery are serially connected and C and L are charged for t<0 period. Then when you turn on the ignition switch you actually disconnect your battery from the circuit. And the charged energy in C and L are driving the transient current to the ignition coil. And as you read above, you have to have your current at a certain value for a limited amount of time (transient). Then your current flow should stop (steady-state). Any system which needs very high energy for a very short period (like pulsed power) needs such transient analysis. Missile launch is just one of many such applications.