Circuits

RC charging

Press Play — the capacitor charges on an exponential curve (τ = RC)

Charge a capacitor through a resistor and watch exponential RC transient behavior. Plot voltage versus time and measure the time constant tau = RC.

RC charging

A capacitor charges exponentially when the circuit is energized. Time constant τ = RC.

Initially current is high; as charge builds, capacitor voltage rises and current falls toward zero.

• τ = RC
• V_C(t) = ε(1 − e^(−t/τ))

Investigation brief

Plan the question before you open the lab

The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.

Driving question

A capacitor charges through a resistor from a 10 V battery. Does its voltage rise at a constant rate, or does it slow down as it approaches the battery voltage?

Predictions to weigh

• The capacitor's voltage rises at a constant rate until it hits 10 V, then stops.
• Charging slows down — the capacitor approaches 10 V but never quite reaches it in finite time (exponential approach).
• The capacitor's voltage overshoots 10 V before settling back down.

Variable roles

What you set:

• Time t (s)

What you measure:

• Time constant τ (s)
• Capacitor voltage V_c (V)

How the investigation runs

1. Open the rc-charging preset and press Reset. R = 100 Ω, C = 0.01 F, giving a time constant τ = RC = 1 s; the battery supplies 10 V.
2. Enable the capacitor-voltage readout.
3. Press Play and record the capacitor's voltage at each listed time.

Governing equation

RC Time Constant — τ = R·C

The time constant τ = RC sets the timescale of an RC circuit's exponential response. After one τ, a charging capacitor reaches about 63% of its final voltage; after about 5τ, it's essentially fully charged.

What the printable worksheet asks students to work out

• For one trial, compute V_c = E(1 − e^(−t/τ)) using E = 10 V, τ = 1 s. Compare to the table.
• At t = τ (1 s), the capacitor reaches about 63% of the final voltage. Explain, using the exponential formula, why it takes many more time constants to get very close to 10 V but never mathematically reaches it exactly.

Where this shows up beyond the lab

• If you doubled the capacitance C (keeping R the same), the time constant τ = RC would double too. Would the capacitor take longer or shorter to reach 63% of 10 V? Why does a bigger capacitor take longer to charge through the same resistor?
• A camera flash capacitor charges slowly (seconds) through a high-resistance path but discharges almost instantly through the flash tube (very low resistance). Explain, using τ = RC, why the charge and discharge times can be so different for the same capacitor.

• AP Physics 2 — Unit 11: Electric Circuits
• AP Physics C: Electricity and Magnetism — Unit 11: Electric Circuits
• IB Physics — B.5 Current and circuits
• General High School Physics — Electricity & DC circuits
• NGSS High School Physics — Electric current and magnetic fields

1. Welcome to Rc Charging
2. Press Play
3. Select the capacitor
4. Exponential charge
5. Open the Properties panel
6. You did it!

Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.

Open Interactive Lab →

Download lab sheet →

Capacitor Charging & Time Constants