When analyzing an RC $($resistor$-$capacitor$)$ circuit where the capacitor is initially uncharged and a DC voltage source is suddenly applied, what describes the voltage across the capacitor over time?

a$)$ The voltage across the capacitor instantly reaches the voltage of the DC source.

b$)$ The voltage across the capacitor gradually increases and asymptotically approaches the voltage of the DC source following an exponential function.

c$)$ The voltage across the capacitor decreases exponentially until it reaches zero.

d$)$ The voltage across the capacitor oscillates before stabilizing at the voltage of the DC source.