**From charging capacitors to filling up water tanks.**

*step*voltage source, only half of the energy coming from the source gets into the capacitor while the other half is dissipated in the circuit resistances and/or lost as radiated electromagnetic energy. In other words, the efficiency is only 50%. Does it always have to happen that way? How can we do better?

The answer lies in

*shaping*the applied voltage. If the rate of rise of the applied voltage is of the order of the time-constant of the circuit, the efficiency is much better than 50%. If it is very slow compared to the time-constant of the circuit, the efficiency approaches 100%. This is proved analytically as well as validated by circuit simulation in this article.
Even if we did not shape the voltage, if the capacitor doesn't have a linear relation between charge and voltage (in other words, it is a non-linear capacitor), the efficiency can still be very different from 50%.

The case of a step current source feeding an inductor is also analogous to the above scenario and gives similar results.

Taking a step back and applying this concept to any other domain (other than electrical engineering) can give some interesting insights. Pumping water into an overhead tank through a pipe having finite resistance (due to friction) is an example of an effort source feeding a potential energy storage element much like a voltage source charging a capacitor. Hence, it will take lesser energy if we were to pump the water slowly (trickle pumping) over several hours rather than doing it fast (gushing water) in fifteen minutes flat!

On a philosophical note, a very nice example is that of a teacher teaching a student. If the teacher goes far too fast beyond the grasping speed of the student, much of the knowledge doesn’t get transferred to the student’s brain.