Charging and Discharging of A Capacitor

Consider resistor `R` and capacitor `C`. The characteristic timescale is: τ=RC called the time constant. Connected to a battery of emf `V₀`: **q(t)=CV₀(1−e⁽−t/RC)) Capacitor voltage: V_C(t)=V₀(1−e⁽−t/RC)) Current: I(t)=V₀R · e⁽−t/RC)** At `t=0`: `q=0` `V<sub>C</sub>=0` current is maximum. As `t→∞`: `q→CV₀` `V_C→V₀` `I→0`.

For initial charge `Q₀`: **q(t)=Q₀e⁽−t/RC) V_C(t)=V₀e⁽−t/RC)** Current magnitude decreases exponentially.

Charging: approximately **63% of final charge/voltage. Discharging: approximately 37%** remains. The textbook's current Chapter 19 structure explicitly includes charging and discharging as its own section. ([Sabaq Foundation][2])

**τ=RC Charging: V_C=V₀(1−e⁽−tτ)) Discharging: V_C=V₀e⁽−tτ)**