Take a look at how the voltage across the capacitor and current through
the circuit (and thus the capacitor) act over time. Notice that when
the voltage is high the current is low and vice-versa. This is a bit
counterintuitive because Ohm's law says that the voltage and current
should always be proportional to each other. A resistor has a constant
resistance and therefore has a constant opposition to current flow. A
discharged capacitor has no opposition to current flow. It looks like a
0 ohm resistor; a short circuit. As a capacitor charges, its opposition
to current flow increases. Once charged it has infinite opposition to
current flow; an open circuit. It acts almost like a resistor that
changes its resistance as it charges. Take another look at the
demonstration circuit at 1 time constant. The capacitor has 6.32 volts
across it and has 3.68 amps of current flowing through it. Danged if it
doesn't look like a 1.72 ohm resistor. However, it only does for that
moment in time. As it charges the resistance appears to increase.

Capacitors do not violate Ohm's law. They just present fewer ohms when
conducting a high current and more ohms when conducting a low current.
This “disconnect” between voltage and current is called phase or phase
angle. We'll learn more about this than we want to in AC circuits.