Understanding RC Circuit Charging

What is the time constant $$\tau$$ of an RC circuit, where $$R$$ is the resistance and $$C$$ is the capacitance?

In an RC circuit, what happens to the voltage across the capacitor as it charges over time?

What is the initial current through the resistor when a capacitor in an RC circuit starts charging?

If the resistance in an RC circuit is doubled, what happens to the time constant $$\tau$$ ?

What is the unit of the time constant $$\tau$$ in an RC circuit?

In an RC circuit, what is the voltage across the capacitor after one time constant $$\tau$$ ?

What is the expression for the voltage across a charging capacitor in an RC circuit as a function of time $$t$$ ?

What happens to the charging time of a capacitor if the capacitance is increased while keeping the resistance constant?

In an RC circuit, what is the final voltage across the capacitor after a long time?

What is the effect of increasing the resistance in an RC circuit on the initial charging current?