3 Topics Covered in Chapter 23 High Voltage Produced by Opening an RL CircuitRC Time ConstantRC Charge and Discharge CurvesHigh Current Produced by Short-circuiting RC CircuitRC Waveshapes
4 Topics Covered in Chapter 23 (continued)Long and Short Time ConstantsCharge and Discharge with Short RC Time ConstantLong Time Constant for RC Coupling CircuitUniversal Time Constant GraphComparison of Reactance and Time Constant
5 Transient Response of an Inductor The transient response of an inductor has a time constant T = L / R.T is in secondsL is in henriesR is in ohmsThe time (T) required for a change in current of 63 % is one time constant, T.Inductor current reaches its steady-state value in five time constants.
6 Transient Response of an Inductor (charge) 10L1 H810 V6R1 kWiC in mA42T = L/R = 1/1 x 103 = 1 msISS = 10 V/1 kW = 10 mAT in msSteady state circuit current (ISS) = 10 mA
7 Interrupting Inductor Current The instant an inductive circuit is opened, a high voltage is generated across the inductor.Opening the circuit causes a rapid decrease in current.In an inductive circuit, the faster the rate of change of current, the higher the amount of induced voltage: vL = L(di/dt).
8 Interrupting Current Flow in an Inductive Circuit Large di/dt generates a very high voltage.
9 Shorting a Charged Capacitor The instant a charged capacitor is shorted with a very low resistance, considerable discharge current flows through the short.Shorting the capacitor causes a rapid decrease in capacitor voltage.In a capacitor circuit, the faster the rate of change of voltage, the higher the amount of current: iC = C(dv/dt).
10 Shorting a charged capacitor With large capacitors,this can be dangerous!
11 Transient Response of a Capacitor The transient response of a capacitor has a time constant T = RC.T is the time in secondsC is the capacitance in faradsR is the resistance in ohmsThe time required for a change in voltage of 63 % is one time constant, T.Capacitor voltage reaches its steady-state value in five time constants.
12 Transient Response of a Capacitor (charge) 101 kW8R10 V61 mFCvC in Volts4Initial charge = 0 V2T in msT = RC = 1 x103 x 1 x 10-6 = 1 ms
13 Transient Response of a Capacitor (discharge) 1081 kWR6vC in Volts1 mFC42Initial charge = 10 VT in msT = RC = 1 x103 x 1 x 10-6 = 1 ms
14 Short Time ConstantsA short time constant is 1/5 or less of the pulse width of the applied voltage.RC Circuits: Produces sharp voltage spikes for vR and rounded edges for vC at the leading and trailing edges of an applied rectangular wave.L/R Circuits: Produces rounded edges for vR and sharp voltage spikes for vL.
15 Short Time Constant in an RC Circuit VS1 kWRVS100 Hz1 mFCvCPulse width = 5 msT = RC = 1 msvR
16 Long Time ConstantsA long time constant is 5 or more times longer than the pulse width of the applied voltage.RC Circuits: vR is very nearly the same as the applied waveform, and the capacitor blocks the average dc level of the applied waveform.L/R Circuits: vR resembles the average dc level of the applied waveform.
17 Long Time Constant in an RC Circuit VS1 kWRVS2.5 kHz1 mFCvCPulse width = 0.2 msT = 1 msvR
18 Output Waveshapes With long time constants: With short time constants: vC and iL rise slowly to the steady-state value.The output waveform is said to be integrated.With short time constants:vC and iL rise rapidly to the steady-state value.The output waveform is said to be differentiated.
19 Integrators and Differentiators VSvOUTvOUTCIntegrators use a relatively long time constant.CvOUTVSRvOUTDifferentiators use a relatively short time constant.
20 Universal Time Constant Graphs Rising curve:Value increases 63% with each time constant.Can represent:Capacitor charging voltage, vCRising inductor current, iLFalling curve:Value decrease 63% with each time constant.Can represent:Capacitor discharging voltage, vCDecaying inductor current, iL