Let a charged capacitor empty through a resistor and the charge does not fall steadily: it decays exponentially, fast at first and ever more slowly, set by a single time constant.
When a capacitor discharges through a resistor, the charge, voltage and current all decay exponentially: x = x₀ e⁻ᵗּᵣᶜ. The time constant τ = RC is the time to fall to 1/e, about 37%, of the starting value.
Adjust R and C to change the time constant and watch the curve stretch or steepen. The dashed line marks one time constant, where the value has dropped to about 37% of where it began.
The product RC has units of seconds and sets the pace of the decay: a larger resistance or capacitance means a slower discharge. After one time constant the value is 1/e (37%) of the start, after about five it is effectively zero. The same exponential, with the same time constant, describes the charge, the voltage and the current.
Four quick checks on exponential discharge and the time constant. Each correct answer earns XP and lights this skill on your star map.
During discharge through a resistor, the charge on a capacitor:
The time constant of a resistor-capacitor discharge circuit is:
After one time constant, the charge has fallen to about:
Doubling the resistance in the discharge circuit:
After one time constant the value falls to 1/e (about 37%), not to half and not to zero. The time constant τ = RC has units of seconds, and a larger R or C means a slower decay. The same exponential and the same τ govern the charge, the voltage and the current.
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