RecallWeave / circuit studies

RC transients · interactive study 02

Charge
takes time.

Follow a capacitor from its starting voltage toward a new source. Change one value, inspect the response, and trace where the energy goes.

Works offline6 worked setups16 practice questions
One resistor, one capacitor and a fixed voltage source The source drives current through resistor R into the marked positive capacitor terminal. The capacitor begins at voltage V0. The source is fixed at Vs after time zero. RVsC+−ivC(0) = V0

Positive current points from the source into the capacitor. A negative value means flow in the opposite direction.

01

Set the circuit

Values after the source step

1 to 1,000,000 ohms

0.001 to 1,000,000 microfarads

−24 to +24 volts; fixed after t = 0

−24 to +24 volts at t = 0

Edits become active when applied.

Start with an example

A 5 V source charges an initially uncharged capacitor. The time constant is 1 second.

Preparing the default circuit…

02

Observe the response

Your applied circuit

Time constant · τ = RC
—One time constant sets the pace.
Time since switching
—Physical time at the cursor.
Decay factor · exp(−t/τ)
—
1.00 τ

Use the slider or its arrow keys. Each step is 0.05 τ; the trace spans 0 to 8 τ.

Voltage approaches the source

Capacitor vCFixed source Vs

Current approaches zero

Signed current iNegative means opposite the marked arrow.
At the selected time
Capacitor voltage vC
Resistor voltage Vs − vC
Signed current i
Charge on marked positive plate
Stored capacitor energy U
Change in stored energy ΔU
Resistor heat since t = 0
Source work since t = 0
Source power delivered
Resistor power dissipated
Energy balance residual

Watch the gap, then the energy

The remaining voltage gap is multiplied by exp(−t/τ). After 1 τ, about 36.8% remains; after 5 τ, about 0.674% remains. A small gap at finite time is still a gap.

vC = Vs + (V0 − Vs) e^(−t/τ)
i = (Vs − V0) e^(−t/τ) / R

Source work = ΔU + resistor heat

Source work is positive for delivery and negative for absorption. The residual is work − ΔU − heat; tiny values can reflect floating-point rounding. Display values are rounded; JSON uses full numerical precision.
Read all 161 sampled values

The same applied response at 0.05 τ intervals. The downloadable observation also includes energy, charge and power in SI units at every sample.

Applied RC response samples
t / τTime / svC / Vi / mA

03 · take the idea with you

Predict first.
Then test your reasoning.

Practice continuity, time constants, signed voltage steps and energy flow with 16 questions. The fixed course stays the same while you explore the lab.

Continue in RecallWeave

  1. Download rc-transients.json using the course button.
  2. Open the RecallWeave offline learner. Under Bring your own lesson, choose the downloaded JSON file.
  3. Check the title and 16-question preview, then select Start this deck. You can cancel the preview first without replacing your current lesson.
  4. Complete the lesson, use review and practice to revisit a missed concept, and keep a note explaining what changed your prediction.

Keep this lab in the repository’s courses folder to use the learner link. The lab and its three downloads work by themselves.