Up until this point, we have been looking at the “Steady State” response of
DC circuits. “Steady-State” implies that nothing has changed in the circuit
in a long time – no power has been turned on or off, no switches have been
flipped, no lightening bolts have hit the circuit, and so on.
In DC “Steady State” conditions, we can treat inductors as short circuits and
capacitors as open circuits. However, when a switch has just been “flipped”
from on to off or off to on, we can no longer make these assumptions about
inductors and capacitors. The time-dependent or DC “Transient” response
of circuits must then be calculated using known behaviors of inductors (V =
L di/dt) and capacitors (i = C dv/dt) and the appropriate mathematics/
calculus.