notes/education/computer engineering/circuits/components/Capacitors.md

A capacitor stores electrical charge. As the charge accumulates on one side of the capacitor, an opposing voltage grows until the voltage between the charged capacitor plate and the input is zero. When the input voltage is removed, the capacitor discharges and current flows out of the charged side of the capacitor, opposing the current that charged it.

Equations

• The current through a capacitor is defined as I = C \frac{d V}{d t}
• The voltage across a capacitor is v(t) = \frac{1}{C} \int_0^t i(\tau) d \tau
• The impedance of a capacitor is Z = \frac{1}{j \omega C}
• A capacitor resists change in voltage
• Voltage cannot change instantly across a capacitor, but current can.
• Voltage across a discharging capacitor is v(t) = v_0 e^{-\frac{t}{R C}}
  • v_0 is initial voltage when discharging begins
  • R is the total resistance faced by the capacitor
  • C is the capacitance of the circuit
• Capacitors in parallel add, and capacitors in series inverse-add $