An RC circuit combines a resistor and a capacitor. This lesson explains how a capacitor charges from a DC voltage source and how the resistor controls the charging process.
A capacitor stores electric charge and energy in an electric field. A resistor limits current. In a simple series RC circuit, a DC source with emf ε, a resistor R, and a capacitor C are connected by a switch. In the charging position, the source supplies energy and charge accumulates on the capacitor plates.
All flashcards
RC time constant
τ=RC sets the characteristic timescale for an RC circuit’s exponential response.
Charging current
For an initially uncharged capacitor, I(t)=(ε/R)e−t/(RC); it starts at ε/R and decays toward zero.
Discharging capacitor voltage
For initial voltage V0, the voltage decays as VC(t)=V0e−t/(RC).
Relaxation oscillator
A circuit that repeatedly charges a capacitor to a threshold, then discharges it through a switch.
RC filter
An RC circuit whose response varies with signal frequency, allowing some frequency components to be reduced.
Quiz questions
For a series RC circuit charging from a source of emf ε, which equation expresses Kirchhoff’s loop rule?Answer: ε−IR−q/C=0
A capacitor with initial charge Q discharges through a resistor R. Which expression gives its charge at time t?Answer: q(t)=Qe−t/(RC)
A capacitor charges from zero toward source voltage ε. What condition must a target voltage VT satisfy to be reached in finite time?Answer: 0<VT<ε
In an ideal RC relaxation oscillator with negligible discharge time, what sets the interval between switching events?Answer: The time required for the charging capacitor to reach the switching threshold.
Why can an RC capacitor charge much more slowly than it discharges?Answer: The effective resistance can be greater during charging than during discharging.
Based on University Physics Volume 2 by Samuel J. Ling, William Moebs, Jeff Sanny (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.