Kirchhoff’s Current Law (KCL) states that the sum of currents entering a node (or junction) in an electrical circuit must equal the sum of currents leaving the node. This is based on the conservation of charge.

KCL Applied to Capacitors

For a capacitor, the current flowing into it is related to the rate of change of voltage across it. The capacitor current is given by:

IC​=CdtdVC​​

where:

• $I_{C}I\_C$IC​ is the capacitor current,
• $CC$C is the capacitance,
• $V_{C}V\_C$VC​ is the voltage across the capacitor,
• $\frac{d{V}_C}{dt}\backslash frac\{dV\_C\}\{dt\}$dtdVC​​ is the rate of change of voltage.

Since a capacitor does not allow direct current (DC) to pass through (it blocks DC after full charge), the sum of currents in a circuit containing capacitors will include both conduction currents (from resistors and other components) and displacement currents (from capacitors).

Implication in Circuits

• In circuits with capacitors, KCL still holds because even though no direct conduction current flows through a capacitor in steady-state DC conditions, a displacement current exists due to the changing electric field.
• In AC circuits, capacitors continuously charge and discharge, creating an alternating current that follows KCL.
• In transient analysis (switching events), the capacitor’s current is dictated by the voltage derivative, ensuring KCL is satisfied.