3 22-1: Response of Resistance Alone Resistance has only opposition to current.There is no reaction to a change.R has no concentrated magnetic field to oppose a change in I, like inductance, and no electric field to store charge that opposes a change in V, like capacitance.
5 22-2: L/R Time ConstantThe action of an RL circuit during the time current builds up to a specific value is its transient response.Transient response is a temporary condition that exists only until the steady-state current is reached.The transient response is measured in terms of the ratio L/R, which is the time constant T of an inductive circuit.T = L/RThe time constant is a measure of how long it takes the current to change by 63.2%.
7 22-3: High Voltage Produced by Opening an RL Circuit When an inductive circuit is opened, the time constant for current decay becomes very short because L/R becomes smaller with the high resistance of the open.Then the current drops toward zero much faster than the rise of current when the switch is closed.The result is a high value of self-induced voltage across a coil whenever an RL circuit is opened.This high voltage can be much greater than the applied voltage.
9 22-4: RC Time ConstantThe transient response of capacitive circuits is measured in terms of the product R x C.To calculate the time constant,T = R x Cwhere R is in ohms, C is in farads, and T is in seconds.
11 22-5: RC Charge and Discharge Curves In Fig. 22-4, the rise is shown in the RC charge curve because the charging is fastest at the start and then tapers off as C takes on additional charge at a slower rate.As C charges, its potential difference increases.Then the difference in voltage between VT and v C is reduced.Less potential difference reduces the current that puts the charge in C.The more C charges, the more slowly it takes on additional charge.Fig. 22-4
13 22-6: High Current Produced by Short-Circuiting RC Circuit A capacitor can be charged slowly by a small charging current through a high resistance and then be discharged quickly through a low resistance to obtain a momentary surge, or pulse of discharge current.This idea corresponds to the pulse of high voltage obtained by opening an inductive circuit.
15 22-7: RC WaveshapesVoltage and current waveshapes in RC circuits can show when a capacitor is allowed to charge through a resistance for RC time and then discharge through the same resistance for the same amount of time.Waveshapes show some useful details about the voltage and current for charging and discharging.
17 22-8: Long and Short Time Constants Useful waveshapes can be obtained by using RC circuits with the required time constant.In practical applications, RC circuits are used more than RL circuits because almost any value of an RC constant can be obtained easily.Whether an RC time constant is long or short depends on the pulse width of the applied voltage.A long time constant can be arbitrarily defined as at least five times longer than the pulse width, in time.A short time constant is defined as no more than one-fifth the pulse width, in time.
19 22-9: Charge and Discharge with Short RC Time Constant Fig illustrates the charge and discharge of an RC circuit with a short time constant.Note that the waveshape of VR in (d) has sharp voltage peaks for the leading and trailing edges of the square-wave applied voltage.Fig. 22-7
21 22-11: Advanced Time Constant Analysis Transient voltage and current values can be determined for any amount of time with a universal time-constant chart.A universal time-constant chart is a graph of curves obtained by plotting time in RC or L/R time constants versus percent of full voltage or current.An example of a universal time-constant chart for RC and RL circuits is shown in Fig (next slide).
23 22-12: Comparison of Reactance and Time Constant Table 22-2Comparison of Reactance XC and RC Time ConstantSine-Wave VoltageNonsinusoidal VoltageExamples are 60-Hz power line, af signal voltage, rf signal voltageExamples are dc circuit turned on and off, square waves, rectangular pulsesReactance XC = 1/(2πfC)Time constant T = RCLarger C results in smaller reactance XCLarger C results in longer time constantHigher frequency results in smaller XCShorter pulse width corresponds to longer time constantIC = VC/XCiC = C(dv/dt)XC makes IC and VC 90° out of phaseWaveshape changes between iC and vC