I can understand the first case above, that seems simple as I can simply measure across the ground and V+, but I am getting very confused for the second case.
Is the capacitor and the resistor in parallel?
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Okay, if you assume no load at all (infinite impedance on V+), the series capacitor gives you an arbitrary offset voltage corresponding to the initial condition of the capacitor. Since there is no load, the capacitor voltage will remain the same forever. Other than that arbitrary voltage you can ignore the capacitor.
If you assume some resistive load, then I think you can calculate it similarly to the first example.