ELC520S: Capacitance and Capacitors Part 2 — Vocabulary (RC Transient)

Vocabulary flashcards covering key RC transient concepts from the notes.

Time constant (τ)

τ = R × C (in seconds). The time constant is the time required for the capacitor voltage to rise toward its final value by about 63%, and for the current to decay toward zero by about 37% of its initial value.

RC circuit

A circuit containing a resistor and a capacitor whose transient response to a step input is exponential, characterized by the time constant τ.

Charging current i(t)

Current while the capacitor is charging: i(t) = (V/R) e^{-t/RC} for a DC supply V across R and C.

Charging voltage v(t)

Voltage across the capacitor while charging: v(t) = V [1 − e^{-t/RC}].

Discharging current i(t)

Current while the capacitor is discharging: i(t) = −(V/R) e^{-t/RC}, i.e., decays in the opposite direction to charging.

Discharging voltage v(t)

Voltage across the capacitor while discharging: v(t) = V e^{-t/RC}.

Initial value (capacitor voltage)

The capacitor voltage at the instant the switch is closed or switched, denoting the start of the transient.

Steady-state value

The final, constant value after the transient has died out; for charging with a DC source, v → V and i → 0.

Thevenin equivalent

A method to replace the external network by a voltage source Vth in series with a resistance Rth, so the capacitor sees τ = R_th C.

Open-circuit equivalent (steady-state)

In DC steady-state, the capacitor behaves as an open circuit; the voltage across it is found from the open-circuit network.

Transient response

The non-steady portion of the circuit's response immediately after switching, which decays over time with time constant τ.

Graphical growth and decay

A graphical method to derive charging curves by drawing tangents and using the time constant to shape the curve.

Voltage across resistor (V_R)

VR = V − v, the drop across the resistor in series with the capacitor.

Initial rate of change of capacitor voltage

At t = 0, dv/dt = V/(R C), i.e., the initial slope of the charging curve.