Time Constant (RC and RL Circuits) Flashcards
A ____________ circuit is characterized by a first-order differential equation.
first-order
In source-free circuits, we assume that the _______ is initially stored in the capacitive or inductive element.
energy
The four typical applications of RC and RL circuits
Delay circuits, relay circuits, photoflash unit, and an automobile ignition circuit.
A ___________ circuit occurs when dc source is suddenly disconnected. The energy already stored in the capacitor is released to the resistors.
source-free RC
A _____ _________ is the manner in which the circuit reacts to an excitation.
Circuit response
We assume to be the voltage v(t) across the capacitor. Since the capacitor is initially charged, we can assume that at time t = 0, the initial voltage is?
V(0) = V_0
We assume to be the voltage v(t) across the capacitor. Since the capacitor is initially charged, we can assume that the corresponding value of energy stored as?
W (0) = 1/2 (CV^(2)_0)
Formula for I_C
(C) (dv/dt) + (V/R) = 0
or
(dv/dt) + (v/RC) = 0
(dv/dt) + (v/RC) = 0 is a first-order DE. Since only the first derivative of v is involved. To solve it, we rearrange the terms as?
(dv/v) = (-1/RC)(dt)
Integrate (dv/v) = (-1/RC)(dt)
ln v = (-t/RC) + ln A
ln v = (-t/RC) + ln A
ln A is the integration constant. Rearrange the equation.
ln (V/A) = (-t/RC)
From the initial conditions, V(0) = A = V_0. What is the value of V(t)?
V(t)= V_0(e^(-t/RC))
It refers to the behavior (in terms of voltages and currents) of the circuit itself, with no external sources of excitation.
natural response of a circuit
The time required for the response to decay to a factor of 1/e or 36.8 of its initial value. Commonly denoted by the lowercase Greek letter tau (τ).
time constant
Time constant is equal to?
τ = RC
V(t) = ?
V_0e^(-t/τ)
