If a capacitor is in parallel with a resistor, is the voltage across the resistor = to the voltage across the capacitor? For example, in this picture Vc = i1(2ohm)

 

To answer your question regardless of the picture, yes, the voltage across the resistor parallel to the cap is equal.

In your picture I don't see any capacitors.

As for what is different in the same parallel circuit - the current is different. The voltage remains equal.

 

By definition, all parallel elements in a circuit must have the same voltage across them.
If not, then they are not in parallel.

 

To answer your question regardless of the picture, yes, the voltage across the resistor parallel to the cap is equal.

In your picture I don't see any capacitors.

As for what is different in the same parallel circuit - the current is different. The voltage remains equal.

In the picture he is doing a steady-state analysis and so replacing the capacitor with an open circuit.

 

Thank you all for the clarification. The concept is like a "day one" thing you learn, but I guess I forgot