# Steady-State DC Analysis: Inductors and voltage sources

Consider the following circuit. I'm tying together the basic definitions of capacitor and inductors, and how they work when connected to a DC source.

First off, we have the equations for current throuh a capacitor, and voltage across a inductor.

• $i_c(t) = C\frac{dv_c(t)}{dt},\quad v_l(t) = L\frac{di_l(t)}{dt}$

Analyzing this, we can see, clearly, that if our inductor and capacitor are "empty" at $t=0$, that our capacitor acts as a short circuit, as there's no current going through it unless there's a change in voltage across the capacitor.

However, I'm having difficulties seeing how the inductor acts as a short circuit. Because we have the DC voltage source $10V$, all we know is that our voltage is constant. What I wonder then is how we can make the statement that our inductor acts as a short circuit.

Also, why do we call direct voltage sources "DC voltage source"? Doesn't is sound a bit strange saying "direct current voltage source"?

• You've asked two unrelated questions. I'd suggest splitting out the one about naming of DC into a separate question. Sep 18 '15 at 19:21