Chapter 21. Ac Circuits
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1 Chapter 21 Ac Circuits
2 AC current
3 Transformer Transforms AC voltage UP or DOWN Historical basis for AC Grid your use George Westinghouse (AC) vs Edison (DC) Losses due to resistance in wire and eddy currents in transformer core Typ eff ~ 95-99%
4 Transformers
5 Transformers II
6 CHAPTER 21: FIGURE 21-3 COLLEGE PHYSICS FREEDMAN RUSKELL KESTEN TAUCK 2014 W. H. FREEMAN AND COMPANY
7 CHAPTER 21: INTRO COLLEGE PHYSICS FREEDMAN RUSKELL KESTEN TAUCK 2014 W. H. FREEMAN AND COMPANY
8 CHAPTER 21: 21-1 COLLEGE PHYSICS FREEDMAN RUSKELL KESTEN TAUCK 2014 W. H. FREEMAN AND COMPANY
9 CHAPTER 21: 21-2 COLLEGE PHYSICS FREEDMAN RUSKELL KESTEN TAUCK 2014 W. H. FREEMAN AND COMPANY
10 CHAPTER 21: FIGURE 21-2 COLLEGE PHYSICS FREEDMAN RUSKELL KESTEN TAUCK 2014 W. H. FREEMAN AND COMPANY
11 CHAPTER 21: 21-3 COLLEGE PHYSICS FREEDMAN RUSKELL KESTEN TAUCK 2014 W. H. FREEMAN AND COMPANY
12 CHAPTER 21: 21-4_2 COLLEGE PHYSICS FREEDMAN RUSKELL KESTEN TAUCK 2014 W. H. FREEMAN AND COMPANY
13 CHAPTER 21: 21-4 COLLEGE PHYSICS FREEDMAN RUSKELL KESTEN TAUCK 2014 W. H. FREEMAN AND COMPANY
14 A full-wave rectifier circuit
15 RC Circuit Exponential Decay An RC circuit is a common circuit used in electronic filters The basic idea is it take time to charge a capacitor thru a resistor Recall that a capacitor C with Voltage V across it has charge Q=CV Current I= dq/dt = C dv/dt In a circuit with a capacitor and resistor in parallel the voltage across the resistor must equal opposite that across the capacitor Hence V c = -V R or Q/C = -IR or Q/C + IR = 0 (note the current I thru the resistor must be responsible for the dq/dt Kirchoff or charge conservation Now take a time derivative dq/dt/c + R di/dt = I/C + R di/dt =0 OR di/dt +I/RC simply first order differential equation Solution is I(t) = I 0 e -t/rc = I 0 e -t/ where = RC is the time constant Voltage across resistor V R (t) = IR = I 0 R e -t/rc = V 0 e -t/rc = - V c (t) voltage across capacitor Note the exponential decay We can also write the eq as R dq/dt + Q/C =0
16 Discharging a capacitor Imagine starting with a capacitor C charged to voltage V 0 Now discharge it starting at t=0 through resistor R V(t) = V 0 e -t/rc
17 Charging a Capacitor Start with a capacitor C that is discharged (0 volts) Now hook up a battery with a resistor R Start the charge at t=0 V(t) = V 0 (1- e -t/rc )
18 RC Circuits Another way Lets analyze this another way In a closed loop the total EMF is zero (must be careful here once we get to induced electric fields from changing magnetic fields) In quasi static case E dl = 0 (voltage sum) over a closed loop Charge across the capacitor Q = CV I = dq/dt = C dv/dt But the same I = -V/R (minus as V across cap is minus across R if we go in a loop) CdV/dt = - V/R or C dv/dt + V/R = 0 or dv/dt + V/RC = 0 Solution is V(t) = V 0 e -t/rc Same solution as before The time required to fall from the initial voltage V 0 to V 0 /e is time = RC
19 Complex impedances Consider the following series circuit If we put an input Voltage V in across the system We get a differential eq as before but with V in V in + IR + Q/C =0 E dl=0 around the closed loop V in + R dq/dt + Q/C = V in + IR + I dt/c we can write the solution as a complex solution I = I 0 e i t V in + IR + I dt/c We can make this more General letting V in = V 0 e i t This allows a driven osc term freq V 0 e i t + R I 0 e i t + I 0 e i t /(i C) V 0 +R I 0 + I 0 /(i C) - thus we can interpret this as a series of impedances (resistance) Z (general impedance ) where Z R = R is the normal impedance of a resistor and Z c = 1/(i C) = -i/( C) is the impedance of a capacitor Note the impedance of a capacitor is complex and proportional to 1/ C - the minus i will indicate a 90 degree phase shift
20 Q26.9 A battery, a capacitor, and a resistor are connected in series. Which of the following affect(s) the maximum charge stored on the capacitor? A. the emf e of the battery B. the capacitance C of the capacitor C. the resistance R of the resistor D. both e and C E. all three of e, C, and R
21 A26.9 A battery, a capacitor, and a resistor are connected in series. Which of the following affect(s) the maximum charge stored on the capacitor? A. the emf e of the battery B. the capacitance C of the capacitor C. the resistance R of the resistor D. both e and C E. all three of e, C, and R
22 Q26.10 A battery, a capacitor, and a resistor are connected in series. Which of the following affect(s) the rate at which the capacitor charges? A. the emf e of the battery B. the capacitance C of the capacitor C. the resistance R of the resistor D. both C and R E. all three of e, C, and R
23 A26.10 A battery, a capacitor, and a resistor are connected in series. Which of the following affect(s) the rate at which the capacitor charges? A. the emf e of the battery B. the capacitance C of the capacitor C. the resistance R of the resistor D. both C and R E. all three of e, C, and R
24 Current in the device I m using right now A desktop PC draws current from a plug to the wall, but what are the details?
25 CHAPTER 21: 21-5 COLLEGE PHYSICS FREEDMAN RUSKELL KESTEN TAUCK 2014 W. H. FREEMAN AND COMPANY
26 CHAPTER 21: FIGURE 21-4 COLLEGE PHYSICS FREEDMAN RUSKELL KESTEN TAUCK 2014 W. H. FREEMAN AND COMPANY
27 CHAPTER 21: 21-6 COLLEGE PHYSICS FREEDMAN RUSKELL KESTEN TAUCK 2014 W. H. FREEMAN AND COMPANY
28 CHAPTER 21: 21-8 COLLEGE PHYSICS FREEDMAN RUSKELL KESTEN TAUCK 2014 W. H. FREEMAN AND COMPANY
29 CHAPTER 21: 21-11_2 COLLEGE PHYSICS FREEDMAN RUSKELL KESTEN TAUCK 2014 W. H. FREEMAN AND COMPANY
30 CHAPTER 21: FIGURE 21-8_2 COLLEGE PHYSICS FREEDMAN RUSKELL KESTEN TAUCK 2014 W. H. FREEMAN AND COMPANY
31 CHAPTER 21: COLLEGE PHYSICS FREEDMAN RUSKELL KESTEN TAUCK 2014 W. H. FREEMAN AND COMPANY
32 CHAPTER 21: TABLE 21-1 COLLEGE PHYSICS FREEDMAN RUSKELL KESTEN TAUCK 2014 W. H. FREEMAN AND COMPANY
33 Resistors in an AC circuit Ohm s Law applied in oscillatory fashion.
34 Inductors in an AC circuit Replace the resistor in the previous slide with an inductor.
35 Because this is a series circuit, the current is the same through the capacitor as through the resistor just considered. Capacitance in an AC circuit
36 Comparing AC circuit elements Summary of circuit elements. Frequency dependence of reactance
37 The loudspeaker, a useful application The woofer (low tones) and the tweeter (high tones) connect in parallel through a crossover.
38 The L-R-C circuit
39 An L-R-C circuit II
40 Power in an inductor Consider current, voltage, and power as functions of time.
41 Circuit behavior at resonance Look at the maximum I when the impedance is a minimum.
42 Tuning a radio LRC circuit tuned to station AM/ FM radio
Chapter 26 DC Circuits
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