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Calculate discharge time constant, voltage decay curve, and time to reach any target voltage.
V(t) = V₀ × e−t/τ
When a charged capacitor is connected across a resistor, it discharges exponentially. The voltage drops according to V(t) = V₀ × e^(−t/τ), where τ = RC is the same time constant used for charging. The key difference is direction: charging approaches Vcc from below, while discharging approaches zero from above.
After one time constant (1τ), the capacitor retains 36.8% of its initial voltage — it has lost 63.2%. After 5τ, only 0.7% remains, which is effectively zero for most practical purposes. The discharge rate depends entirely on R and C: a larger resistor or capacitor means slower discharge.
Discharge timing is fundamental to many circuits. Monostable timers (like the 555) use RC discharge to set pulse width. Touch sensors detect discharge rate changes caused by finger capacitance. Sample-and-hold circuits rely on slow discharge through high-impedance buffers to maintain a voltage reading.
Discharge Voltage
V(t) = V₀ × e−t/τTime Constant (τ)
τ = R × CDid you know? RC time constants appear everywhere in nature — the electrical decay of a neuron's membrane potential follows the same RC exponential curve. Neurologists use the concept of "membrane time constant" to model how quickly neurons respond to stimuli.