Watch a capacitor charge
You will be able to: Relate RC time constant to charging voltage, current and stored energy.
Why does charging current slow down?
Connect an initially uncharged capacitor to a battery through a resistor. At first the capacitor has no voltage, so the resistor has the full source voltage. As charge gathers on the plates, capacitor voltage rises and leaves less voltage to drive current through the resistor.
A useful starting point: Capacitors combine differently from resistors →
Words and symbols before equations
- Time constant τ
- Characteristic time RC in seconds; Ω×F has units of seconds.
- Initial condition
- The capacitor voltage just before switching; here it is zero.
- Asymptote
- A value a curve approaches gradually rather than reaching abruptly.
- Charging current
- Conventional current toward the plate becoming positive; it decreases during this simple charging process.
What this picture assumes
One ideal 10 V source, series resistor and initially uncharged capacitor. No leakage. Curves use exponential charging; the key AP ideas are time constant, trends and limiting values. Charge is plate-charge magnitude.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- τ=1 s; t/τ=1. V_C=6.321 V, |I|=0.3679 mA, |Q|=632.1 μC. Stored energy=1.998 mJ; cumulative resistor heat=4.323 mJ.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
AP scope: explain RC trends and graphs qualitatively and calculate initial and final states. The simulation supplies intermediate values for exploration; deriving or memorizing time-dependent exponential equations is not required in AP Physics 2.
The loop gives ε=IR+V_C at every time. Initially V_C=0, so I₀=ε/R. After a long time V_C approaches ε and the charging branch current approaches zero.
After one time constant, capacitor voltage and charge reach about 63% of their final values; current falls to about 37% of its initial value. Increasing R slows charging and lowers initial current. Increasing C slows charging and increases final charge but leaves initial current unchanged.
Optional model detail, beyond the required AP time-dependent mathematics: the simulation uses V_C=ε(1−exp(−t/RC)) and I=(ε/R)exp(−t/RC). You can reason from the curve and endpoints without memorizing the exponential. Stored energy U=½CV_C² rises; in a complete ideal charging event from zero, half the source’s supplied energy remains in the capacitor and half becomes resistor heat.
A worked example, step by step
Charge 100 μF through 10 kΩ from a 10 V source. Find τ, initial current and values at one τ.
- Convert R=10,000 Ω and C=100×10⁻⁶ F. Then τ=RC=1.0 s.
- I₀=10/10,000=1.0 mA.
- At t=τ: V_C≈6.32 V and I≈0.368 mA.
- Final Q=Cε=1000 μC; at τ it is about 632 μC.
One time constant is not the time to finish charging. It marks about 63% of the final charge.
Double C with R and ε fixed. Does initial current double?
Compare with an explanation
No. I₀=ε/R is unchanged; τ and final charge double.
Predict. Change one thing. Explain.
Predict separately what doubling R or C changes: time scale, initial current and final charge. Move time to one τ and compare the graph with the numerical readout.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
τ=1 s; t/τ=1. V_C=6.321 V, |I|=0.3679 mA, |Q|=632.1 μC. Stored energy=1.998 mJ; cumulative resistor heat=4.323 mJ.
One ideal 10 V source, series resistor and initially uncharged capacitor. No leakage. Curves use exponential charging; the key AP ideas are time constant, trends and limiting values. Charge is plate-charge magnitude.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant current, voltage or energy relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionA 200 μF capacitor charges through 5 kΩ from 6 V. (a) Find τ. (b) Find initial current. (c) Find final charge. (d) State V_C at τ.
This response is not submitted or saved. Copy it before leaving.
Compare with the answer and four-point rubric
- 1 point: τ=(5000)(200×10⁻⁶)=1 s.
- 1 point: I₀=1.2 mA.
- 1 point: Q_final=1200 μC.
- 1 point: V_C≈0.632×6=3.79 V.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What determines charging speed?
The time constant RC.
RECALL 2Why does current decrease?
Rising capacitor voltage reduces the resistor’s voltage drop.
RECALL 3Does steady zero capacitor-branch current imply zero capacitor voltage?
No. It can retain a nonzero voltage and stored energy.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Watch a capacitor charge
- τ=RC.
- Initially uncharged: I₀=ε/R; long time: V_C→ε, I→0.
- At t=τ: V_C≈0.632ε; I≈0.368I₀.
- U_C=½CV_C².
Remember: One time constant is not the time to finish charging. It marks about 63% of the final charge.
Conditions: One ideal 10 V source, series resistor and initially uncharged capacitor. No leakage. Curves use exponential charging; the key AP ideas are time constant, trends and limiting values. Charge is plate-charge magnitude.
Refresh Kid · AP Physics 2 Unit 3 (official Unit 11) · Objectives 11.8.B · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 11.8, objectives 11.8.B. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Refresh Kid calls this the third AP Physics 2 unit; College Board numbers it Unit 11; the first unit in this course is official Unit 9. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
Want to work through this with a tutor?
Bring your question about Watch a capacitor charge. Your explanation and answers remain free to access.