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

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-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.
+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 $Z = \frac{1}{j \omega C}$