What you are looking at
A battery charges a capacitor through a resistor. The blue plates fill with charge, the current dots show the
flow (bright when large, fading as it dies), and the graph traces the capacitor voltage (green) and current
(orange) over time. Switch between
charge,
discharge and
open to see the curves reverse and flatten.
Why the curve bends
At the instant you connect the battery, the empty capacitor offers no back-voltage, so the full EMF drives a
large current I = V/R. But every bit of charge that arrives raises the capacitor's voltage, which opposes the
battery, shrinking the current. The result is exponential:
V_C(t) = V (1 − e^(−t/RC)), I(t) = (V/R) e^(−t/RC)
The voltage rushes up, then eases toward the battery value; the current starts at its maximum and decays
away. Discharging is the mirror image — the capacitor drives current back through R and both fall
exponentially to zero.
The time constant
One number sets the pace: the
time constant
τ = R · C
In one time constant the capacitor reaches
63% of the way to its final voltage (the gold
line on the graph); after about 5τ it's essentially fully charged. A bigger resistor throttles the current;
a bigger capacitor holds more charge — either one makes the charging slower. This same τ sets the blink rate
of timers, the smoothing in power supplies, and the tone controls in audio gear.
Things to try
Charge fully, then hit discharge and watch both curves fall. Increase R or C and see τ grow and everything
slow down; the 63%-at-τ mark always lands in the same place relative to τ. Raise the battery EMF and the
whole curve scales up while its shape — and τ — stay the same.