RC Charging: A Capacitor's Exponential Approach

1 · Predict

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?

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

2 · Set Up

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.

3 · Collect Data

Plot capacitor voltage V_c (y-axis) against time t (x-axis) for your three readings. Does the curve flatten out as it approaches 10 V?

4 · Analyze

1. For one trial, compute V_c = E(1 − e^(−t/τ)) using E = 10 V, τ = 1 s. Compare to the table.
2. 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.

5 · Extend

1. 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?
2. 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.

The Physics Behind This Experiment

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