The transient response of an inductive circuit with nonsinusoidal current is indicated by the time constant L/R. With L in henrys and R in ohms, T is the time in seconds for the current iL to change by 63%. In five time constants, iL reaches the steady value of VT/R.
At the instant an inductive circuit is opened, high voltage is generated across L because of the fast current decay with a short time constant. The induced voltage vL= L(di/dt). The di is the change in iL.
The transient response of a capacitive circuit with nonsinusoidal voltage is indicated by the time constant RC. With C in farads and R in ohms, T is the time in seconds for the voltage across the capacitor vC to change by 63%. In five time constants, vC reaches the steady value of VT.
At the instant a charged capacitor is discharged through a low resistance, a high value of discharge current can be produced. The discharge current iC = C(dv/dt) can be large because of the fast discharge with a short time constant. The dv is the change in vC.
The waveshapes of vC and iL correspond, as both rise relatively slowly to the steady-state value.
Additionally, iC and vL correspond because they are waveforms that can change instantaneously.
The resistor voltage vR = iR for both RC and RL circuits.
A short time constant is one-fifth or less of the pulse width, in time, for the applied voltage.
A long time constant is greater than the pulse width, in time, for the applied voltage by a factor of 5 or more.
An RC circuit with a short time constant produces sharp voltage spikes for vR at the leading and trailing edges of a square-wave of applied voltage. The waveshape of voltage VT is across the capacitor as vC. See Fig. 22–7.
An RC circuit with a long time constant allows vR to be essentially the same as the variations in applied voltage VT, and the average dc value of VT is blocked as vC. See Fig. 22–8.
The universal rise and decay curves in Fig. 22–9 can be used for current or voltage in RC and RL circuits for any time up to five time constants.
A differentiator is a circuit whose output voltage is proportional to the change in applied voltage.
An integrator is a circuit whose output combines, or integrates, its original voltage with the new change in voltage.
The concept of reactance is useful for sine-wave ac circuits with L and C.
The time constant method is used with L or C to analyze nonsinusoidal waveforms.
