Why it is the same i throughout the circuit

An observation that helps in writing a single $i(t)$ in the equations: in a single-loop circuit (only one loop) the current $i$ has the same instantaneous value at every point of the circuit. This is true even through the capacitor, even though charges do not physically pass through it: the insulator between the plates prevents that.

What happens is that charges accumulate on one plate and leave the other at the same rate. So, from the “point of view” of the external wires, everything behaves as if the current passed through the capacitor continuously. This is why we write a single $i(t)$ in the LC and RLC equations, with the relation to $Q(t)$ being $\pm\,dQ/dt$ depending on how we have oriented the current arrow relative to the plate we call $+Q$.

Continuity

The continuity equation for charge is the electrical cousin of mass conservation in fluids: the same idea underlying Kirchhoff’s first law for nodes.

Collegamenti

Argomenti: Electromagnetic induction Concetti: LC and RLC oscillations · Kirchhoff’s laws

Esercizi collegati: Problem — Natural frequency of an LC circuit · Problem — Capacitor of an AM radio receiver · Worked exercise — Forced RLC, find the generator’s EMF