RC Circuits Vocabulary Flashcards

Vocabulary flashcards covering RC circuits, charging and discharging dynamics, and the meaning of the time constant.

RC circuit

A circuit containing resistors and capacitors in which the current varies with time; the resistance (R) and capacitance (C) determine how quickly the capacitor charges or discharges.

Resistor

A passive component that resists current flow and drops voltage according to V = I R.

Capacitor

A device that stores electrical energy as charge; Q = C V, and its voltage changes as it charges or discharges.

Capacitance (C)

The ability of a capacitor to store charge per volt; unit: farad (F); relation Q = C V.

Time constant (τ)

τ = R C; the characteristic time for charging or discharging; a larger τ means a slower change.

Exponential decay

A decrease that follows V(t) = V0 e^{−t/τ} or I(t) = I0 e^{−t/τ}, typical for RC discharging.

Charging

Process when the switch closes and the capacitor voltage rises toward the source_emf ε while current decreases over time.

Discharging

Process when the capacitor releases stored energy through the resistor, causing voltage to decay toward zero.

Emf (ε)

The source electromotive force or supply voltage in the circuit.

Initial conditions (charging from uncharged)

For charging from an uncharged capacitor: Vc(0) = 0, Q(0) = 0, I(0) = ε / R.

Voltage across capacitor during charging (Vc(t))

Vc(t) = ε [1 − e^{−t/RC}].

Current during charging (I(t))

I(t) = (ε / R) e^{−t/RC}.

Charge during charging (Q(t))

Q(t) = C ε [1 − e^{−t/RC}].

Voltage across resistor during charging (VR(t))

VR(t) = ε − Vc(t) = ε e^{−t/RC}.

One time constant (t = τ)

At t = τ, Vc ≈ 0.632 ε and I ≈ 0.368 (ε/R); the circuit has progressed by roughly one time constant.

Final steady-state in charging

As t → ∞, Vc → ε and I → 0; the capacitor becomes fully charged to the source voltage.

Discharging time constant (τ)

τ = RC also governs capacitor discharge when the source is removed.

Q = C V relationship

Charge on the capacitor is Q = C Vc.

Discharging voltage equation

Vc(t) = V0 e^{−t/RC} for a capacitor discharging from initial voltage V0.

Discharging current equation

I(t) = (V0 / R) e^{−t/RC} for a capacitor discharging from initial voltage V0.

Effect of R and C on speed

Increasing R or C increases τ (slower charging/discharging); decreasing them reduces τ (faster).