ELEC1111 · W3 · lecture
RC Transient
Charging, discharging, and the time constant τ.
~45 min
note
Lecture summary
A first-order RC circuit responds to a step input with an exponential of time constant τ = RC. Voltage across the capacitor charges towards the source value and discharges towards zero along the same exponential curve.
example
Worked example: charging curve
Given R = 10kΩ and C = 1µF, τ = 10ms. After 5τ ≈ 50ms the capacitor is within 1% of its final value. Use v(t) = V_s (1 − e^(-t/τ)) for charging from a discharged state.
note
Common mistakes
Forgetting to include the source impedance, mixing up charging vs discharging signs, and reading the time axis on the oscilloscope at the wrong scale.
lab guide
Lab measurement method
Drive the RC network with a square wave at a frequency such that T/2 ≫ 5τ, capture both channels on the oscilloscope, and read τ at 63.2% of the final value.