Capacitor Charge and Discharge Knowledge

• Capacitor charging is a process where voltage gradually increases, eventually reaching the source voltage. The charging voltage formula is V(t) = V_s * (1 - e^(-t / RC)), where V_s is the source voltage.
• Capacitor discharging is a process where voltage gradually decreases, eventually dropping to zero. The discharge voltage formula is V(t) = V₀ * e^(-t / RC)), where V₀ is the initial voltage.
• The time constant τ (tau) of an RC circuit equals resistance R multiplied by capacitance C (τ = R * C). It represents the time required for the capacitor voltage to reach approximately 63.2% of the source voltage during charging, or drop to approximately 36.8% of the initial voltage during discharging.
• The formula for capacitor charging current is I(t) = (V_s / R) * e^(-t / RC).
• The formula for capacitor discharging current is I(t) = -(V₀ / R) * e^(-t / RC). The negative sign indicates the current direction is opposite to that during charging.
• The charge stored in a capacitor is Q = C * V, and the stored energy is E = 0.5 * C * V².
• In an RC circuit, after approximately 5 times the time constant (5τ), the capacitor charging or discharging process is essentially complete, reaching a steady state.