Physics · Circuits

RC Charging and Discharging

Simulation loading

Open Model Lab is preparing the live lab, controls, and graph surface for this concept.

Wrap-up

What you learned

Recommended next: Open concept testCheck whether the core ideas are ready without leaving this concept.
Read next: Power and Energy in CircuitsCompare steady power with transient storage

Key takeaway

At 1τ, a charging capacitor has made a predictable partial move: about 63% of the voltage rise is complete while current has fallen to about 37% of its starting value.
Charging starts with the largest current because the capacitor voltage is initially zero; as capacitor voltage rises, resistor drop and current both shrink.

Common misconception

A capacitor connected to a battery should jump to the battery voltage immediately because the source voltage is already fixed.

The source voltage is fixed, but the resistor limits how quickly charge can move onto the capacitor plates.

Keep the time-response story moving

Keep this idea moving

Open the next concept, route, or track only when you want the current model to widen into a larger branch.

Compare steady power with transient storageCircuits

Power and Energy in Circuits

Keep one source and one resistive load in view while current, power, and accumulated energy over time stay tied to the same honest circuit.

Review the storage modelElectricity

Capacitance and Stored Electric Energy

Keep one parallel-plate capacitor on screen so geometry, stored charge, field strength, and stored electric energy stay tied to the same bounded battery-and-plates model.

Next in Non-ideal source behaviorCircuits

Internal Resistance and Terminal Voltage

Keep one non-ideal source and one load on screen so emf, internal drop, terminal voltage, current, and wasted power stay tied to the same one-loop circuit.

Stay with this concept

Review, test, or free-play here when you want one more same-concept pass.

More practice optionsReview on the bench · Worked examples

Practice optionReview on the benchReplay the guided setup with the key controls and graphs in sight.
Practice optionWorked examplesCompare against solved walkthroughs after you try the setup yourself.
Practice optionFree play on the benchExperiment freely with the live controls before moving to another concept.

Reference and support

Use these calmer sections when you want a fuller explanation, examples, or accessibility support after the guided flow.

Return here when you want the slower reference pass.

Open reference and support

Equation snapshotTime constant · Charging capacitor voltageShow 2 equations

Time constant
$τ = R C$
The product of resistance and capacitance sets how quickly the RC response happens.
Charging capacitor voltage
$V_{C} = V_{s} (1 - e^{- t / τ})$
The capacitor voltage rises toward the source value instead of jumping there instantly.

Why it behaves this way

Explanation

An RC circuit turns capacitor storage into a time-response story. The resistor limits how fast charge can move, the capacitor stores that charge as voltage builds across its plates, and the time constant tau = RC tells you whether the response is fast or slow.

This bench stays intentionally small: one battery, one resistor, one capacitor, and one charge-versus-discharge toggle. That is enough to show why capacitor voltage does not jump instantly, why current is largest right at the start, and how stored energy follows the same changing voltage without turning the page into a general transient-circuit simulator.

Key ideas

01At 1τ, a charging capacitor has made a predictable partial move: about 63% of the voltage rise is complete while current has fallen to about 37% of its starting value.

02Charging starts with the largest current because the capacitor voltage is initially zero; as capacitor voltage rises, resistor drop and current both shrink.

03The time constant tau = RC sets the pace. Larger resistance or larger capacitance both make charging and discharging slower.

Worked examples

Live RC checks

Open examples when you want to see the same idea walked through step by step.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Use the exact RC setup on screen. The same source voltage, resistance, capacitance, mode, and inspected time drive the equations below.

Supporter unlocks saved study tools, exact-state sharing, and the richer review surfaces that support this guided flow.

View plans

Example 1 of 2

Frozen valuesFrozen at 0.00

For the current RC setup, what is the time constant, and what capacitor voltage follows at the current inspected time?

R

Resistance

2 ohm

C

Capacitance

1 F

t

Elapsed time

0 s

1. Build the time constant

τ = R C = 2 \times 1 = 2

2. Use the live mode rule

This setup is charging, so

V_{C} = V_{s} (1 - e^{- t / τ})

3. Substitute the live values

V_{C} = 8 (1 - e^{- 0/2})

4. Read the capacitor voltage

That gives

V_{C} = 0

t = 0

Time constant and capacitor voltage

τ = 2, V_{C} = 0

The capacitor voltage is still climbing quickly because the first time constant has not finished yet.

Quick test

Loading saved test state.

Accessibility

Open the text-first descriptions when you need the simulation and graph translated into words.

The simulation shows one battery, one resistor, and one capacitor in a bounded RC loop. A mode toggle switches between charging and discharging, while sliders set source voltage, resistance, and capacitance.

Overlays can show current flow, voltage labels, tau markers, plate charge build-up, and stored-energy cues. The same controls drive the stage, readout card, and both graphs.

Graph summary

The voltage graph shows capacitor voltage and resistor drop against time so the changing loop balance stays visible. The normalized-response graph shows charge fraction, current fraction, and stored-energy fraction against the same time axis so the RC pace is easy to compare.

Bench tools and share links

Keep stable concept links and exact-state sharing tucked away until you actually need to relaunch or share the bench.

Try this setup

Jump to a named bench state or copy the one you are looking at now. Shared links reopen the same controls, graph, overlays, and compare context.

Featured setups

1τ checkpoint

Open the reference setup at 1τ so the 63% voltage and 37% current markers are visible together.

Slow response

Increase the RC product and compare how the same source voltage takes longer to build capacitor voltage.

Discharge reversal

Switch to discharge and watch the charged capacitor drive reversed current while stored energy drains away.

Saved setups

Saved setups are a Supporter study tool. Stable concept links still work for everyone.

Checking saved setup access

Open Model Lab is resolving whether this bench can save locally, sync to an account, or open Supporter-only compare tools.

Copy current setup

Exact-state sharing is part of Supporter. Stable concept and section links still stay available.

Stable links

Progress and next steps

Keep progress signals, starter-track handoffs, and review prompts available without letting them compete with the live lesson flow.

Progress

Loading progress

Loading saved concept progress for this browser or synced account before showing completion status.