Section 28.9
Discharging a capacitor is really a circuit with two components: a resistor
and a capacitor. The resistor could be the equivalent resistor of any
combination of resistors.
The Kirchhoff loop equation for the circuit (eq 28.25) + definition of current
as the derivative of charge (eq 28.6) lead to the equation
\frac{dQ}{dt}+\frac{Q}{RC}=0
and the solution to this is the exponential decay with time constant
\tau = RC
When a capacitor discharges, the charge, voltage and current all exponentially
decrease. When a capacitor charges, the voltage and charge increase but the
current still decreases. The end current through the capacitor of an RC
circuit is always zero in both charging or discharging.
The quantities described in this section refer to the current, charge and
voltage on the capacitor. Be careful not to apply these formulas to the entire
circuit. If the capacitor is in parallel with a resistor for example, the end
current after a long time on the capacitor will be zero (whether charging or
discharging) but there could be a non-zero current on the parallel resistor.
Example 28.12 is important in this section while challenge example 28.13 is
more advanced than what you need for this course.
Check your understanding: RC Circuits.