April 2026Guided SimulationBeginner

Capacitor Charging Circuit — Step by Step

Understanding how a capacitor charges and discharges is essential to electronics. The RC time constant governs timing in 555 timer circuits, smoothing in power supplies, and sampling in ADCs. This guided simulation makes it visual and interactive.

What you will learn: RC time constant calculation, exponential charge/discharge behaviour, how to use a scope in the simulator to see waveforms, and why this matters in every timing circuit you will ever build.

Circuit Diagram

graph LR V["Voltage Source (Vs)"] --> SW["Switch (closes at t=0)"] SW --> R["Resistor (R)"] R --> C["Capacitor (C)"] C --> GND["GND"] V --> GND PROBE["Scope probe — measure Vc here"] -.->|monitor| C style V fill:#1a3a4a,stroke:#00e5ff,color:#00e5ff style C fill:#2a1a3a,stroke:#aa88ff,color:#aa88ff style GND fill:#161b1f,stroke:#5a7080,color:#5a7080

Key formula: V_c(t) = Vs × (1 − e^−t/RC)

Where τ = RC is the time constant. After 1τ the capacitor reaches 63.2% of Vs. After 5τ it is considered fully charged (99.3%).

Step-by-Step Guide

STEP 1

Calculate the Time Constant

Pick values and calculate τ = R × C before simulating. Example: R = 10kΩ, C = 100µF

τ = 10,000 × 0.0001 = 1 second

This means after 1 second the capacitor will be at 63.2% of the supply voltage. After 5 seconds (5τ), it is fully charged. This is a slow enough charging rate to watch in real time in the simulator.

💡 Think of it like filling a bucket with a garden hose: At first, water rushes in quickly because the bucket is empty and the pressure difference is high. As the bucket fills up, the pressure equalises and flow slows down. The bucket never quite fills the last few drops — it just keeps slowing. That's exactly how a capacitor charges through a resistor.

Quick τ reference: 1kΩ + 1µF = 1ms. 10kΩ + 100µF = 1s. 1MΩ + 1µF = 1s. The product R×C always gives seconds when R is in ohms and C is in farads.

STEP 2

Open the Simulation and Add a Scope

Open the capacitor simulation below. The circuit shows a voltage source, resistor, and capacitor. Click Run to start charging.

To add an oscilloscope: click Scope → New Scope, then click on the capacitor to probe it. You will see the exponential charge curve building in real time on the scope display.

▶ Open Capacitor Charging Sim

What to look for: The charge curve is NOT linear. It rises quickly at first, then slows as the capacitor voltage approaches the source voltage. This is the exponential nature of RC charging.

STEP 3

Measure the Time Constant

With the scope running, identify the time when the capacitor voltage reaches 63.2% of the supply voltage. With a 5V supply, that is at 3.16V.

If R = 10kΩ and C = 100µF, this should occur at exactly t = 1 second. Verify this in the simulation by reading the scope horizontal axis.

⚠️ Common misconception: The capacitor is NOT halfway charged at t = 0.5τ. At 0.5τ it is at 39.3%. At τ it is at 63.2%. The "halfway" point is actually at 0.693τ. The exponential means it charges faster early on.

STEP 4

Observe the Discharge

In the simulator, pause the simulation once the capacitor is fully charged. Then change the voltage source to 0V (or disconnect it) to watch the capacitor discharge through the resistor.

Discharge equation: V_c(t) = V0 × e^−t/RC. After 1τ the voltage drops to 36.8% of its initial value. After 5τ it is essentially zero.

▶ Capacitor Basic Demo

STEP 5

Change Component Values — Experiment

Double-click R and change to 1kΩ. The time constant drops to 0.1 seconds — watch how much faster charging happens. Change C to 10µF for a τ of 10ms — near-instant on the simulator timescale.

Then try: R = 1MΩ, C = 1µF. τ = 1 second again — same time constant, same curve shape, completely different component values. This demonstrates that only the RC product matters, not individual values.

Real-world uses of RC timing: 555 timer frequency (τ sets high and low times), power supply startup delays, switch debounce filters, ADC sample-and-hold timing, and camera flash capacitor charge indicators.

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Frequently Asked Questions

What is the RC time constant?

The RC time constant (τ = R × C, in seconds) is the time it takes a capacitor to charge to 63.2% of the supply voltage, or discharge to 36.8% of its initial voltage, through a resistor. After 5τ, the capacitor is considered fully charged or discharged.

Why does a capacitor charge exponentially and not linearly?

As the capacitor charges, its voltage rises, reducing the voltage difference across the resistor. Less voltage difference means less current flows. Less current means slower charging. This feedback creates the exponential curve: fast at first, progressively slower as it approaches the target voltage.

Can a capacitor power a circuit temporarily?

Yes. A fully charged capacitor acts as a temporary voltage source that discharges through the load. Large capacitors (called bulk capacitors) in power supplies hold charge during brief power interruptions. Supercapacitors (1F to thousands of farads) can power small circuits for minutes to hours.

Frequently Asked Questions

What is the RC time constant?

The time constant τ = R × C (in seconds, with R in ohms and C in farads) is the time for a capacitor to charge to 63.2% of the supply voltage or discharge to 36.8% of its initial voltage. After 5τ, the capacitor is considered fully charged or discharged.

Why does a capacitor not charge linearly?

As the capacitor charges, the voltage across the resistor decreases, reducing current flow, which in turn slows further charging. This feedback produces exponential behaviour: fast at first, progressively slower as it approaches the target voltage.

How large a capacitor do I need for a power supply filter?

Use C = I_load / (2 × f × V_ripple). For 500mA load, 50Hz mains, 0.5V ripple: C = 0.5 / (2 × 50 × 0.5) = 10,000µF. Larger capacitors mean less ripple but more inrush current at power-up.