I am in the process of completing some homework and have come across a question that says: "What is the steady-state current?" It is asking in reference to a circuit that includes two capacitors in parrallel and a DC source of 24V and an AC source given by $\epsilon = 20 \cos(120 \pi t)\ \text{V}$, where $t$ is in seconds. I assume that it is asking when the current is constant. Because naturally the current is not constant due to the AC source, would I just consider the DC source for this?
Answer
Steady state means, in this context, ignoring transients due to initial conditions.
For a capacitor, the steady state current due to a DC voltage source is zero.
The steady state current due to an AC source is simply the (constant) amplitude of the sinusoidal current.
To be clear, the current is changing in time and so is not constant. But, the amplitude of the current is constant, i.e.,
$$i_C = A \cos(\omega t + \phi)$$
where $A$ is a constant. This is called AC or sinusoidal steady state.
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