high School⏱ 4 min

RC Charging

Exponential charging of an RC circuit

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10 V4 kΩ500 µFV₀t (5τ)V꜀ = 0.0 V · I = 2.50 mA

Parameters (V₀ = 10 V)

VC=V0(1−e−t/RC)V_C = V_0\left(1 - e^{-t/RC}\right)

τ = RC = 2.00 s

• The capacitor charges fast at first, then ever slower • The current decays toward zero as it charges • After τ = RC it reaches ~63 %, after 5τ essentially full