Lesson 13 of 15

RC Time Constant

RC Circuits

A resistor and capacitor in series form an RC circuit. When charged or discharged, the voltage decays exponentially with time constant:

au=RC au = RC

  • au au (tau) — time constant (seconds)
  • R — resistance (Ω)
  • C — capacitance (farads, F)

What τ Means

After one time constant au au, the voltage has decayed to 1/e ≈ 36.8% of its initial value. After 5au5 au it is essentially zero (0.7%).

TimeVoltage remaining
0100%
au au36.8%
2au2 au13.5%
5au5 au0.7% (fully discharged)

Charging and Discharging

extDischarging:V(t)=V0e−t/au ext{Discharging: } V(t) = V_0 e^{-t/ au}

ight)$$ ### Applications RC time constants set the frequency response of filters and timing circuits — camera flashes, audio tone controls, oscillator timing, and signal debouncing. ### Examples | R (Ω) | C (F) | τ (s) | |-------|-------|-------| | 1000 | 1×10⁻³ | **1.0000** | | 10000 | 100×10⁻⁶ | **1.0000** | | 1000 | 1×10⁻⁶ | **0.0010** | | 470 | 100×10⁻⁶ | **0.0470** | ### Your Task Implement `rc_time_constant(R, C)` returning $ au$ in seconds.
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