first hooked up, the capacitor is empty—it is ready and waiting for as much charge as can flow to it. Thus,
initially, the circuit behaves as if the capacitor weren’t there. In this case, then, the current through the
resistor starts out at 10 V/5 Ω = 2 A.
But, after a long time, the capacitor blocks current. The resistor might as well not be there; we might
as well just have a capacitor right across the battery. After a long time, the capacitor takes on the voltage
of the battery, 10 V. (So the charge stored on the capacitor is Q = CV = 10 C.)
RC Circuits: Transitional Behavior
Okay, the obvious question here is, “What happens during the in-between times, while the capacitor is
charging?” That’s a more complicated question, one that is approached in Physics C. It’s easiest if we
start with a discussion of a capacitor discharging . (See Figure 19.11 .)
Figure 19.11 Graph of a capacitor discharging.Consider a circuit with just a resistor R and a capacitor C. (That’s what we mean by an RC circuit.)
The capacitor is initially charged with charge Q 0 . Apply Kirchoff’s voltage rule:
−IR + V (^) c = 0
where V (^) c is the voltage across the capacitor, equal to Q /C by the equation for capacitors.
By definition, current is the time derivative of charge,
So substituting this value for I into the Kirchoff equation we wrote above, and rearranging a bit, we get