RC Charging Circuit Lab

A capacitor stores charge; a resistor limits how fast it can flow. Put them together and you get the most important timing circuit in electronics — one that sets the heartbeat of everything from camera flashes to computer clocks.

The exponential law

Charge does not pile up linearly. As the capacitor fills, it pushes back harder against the incoming current, so the flow slows. The result is an exponential approach:

• Charging: V(t) = V₀ (1 − e^−t/RC)
• Discharging: V(t) = V₀ e^−t/RC

The product τ = RC is the time constant, measured in seconds (ohms × farads). It has a very clean meaning:

• After 1τ, charging reaches 63.2% of final (or discharging falls to 36.8%).
• After 3τ, about 95%.
• After 5τ, over 99% — treated as “done” in practice.

Reading the graph

The shape is the same whether you charge or discharge, just flipped. Notice that the curve is steepest at the start of charging — current is maximum when the capacitor is empty, because nothing is pushing back yet. As voltage builds, current decays with the same exponential law.

Try this

• Double R and the charging takes twice as long — τ scales directly with resistance.
• Double C and it also takes twice as long — a bigger bucket fills slower at the same flow rate.
• Find the 63.2% mark on the curve and check that the elapsed time equals R × C.

Why it matters

RC circuits are everywhere timing matters: the debounce circuit that stops a single keypress registering ten times, the low-pass filter that smooths a power supply, the coupling capacitor that passes audio but blocks DC, and the delay that holds a microcontroller in reset at power-up. The same exponential governs radioactive decay, drug elimination from the bloodstream, and a cooling cup of coffee.