11/13/2018

LECTURE 19 AC Generators AC Circuits Start by considering simple circuits with one element (R, C, or L) in addition to the driving emf. It will lead to Oscillations and Driven RLC circuits

Alternating Current Generators (DEMO) (N = 2 for this coil) DEMO: New AC Motor – coil, magnetic & light bulb – faster I crank the brighter the bulb 11/13/2018

Phasors for R V in phase with I 11/13/2018

Power Dissipated in a Resistor Peak value Average value 11/13/2018

Standard Alternating Voltage in the US +peak -peak 11/13/2018

Using rms values: summary Using rms values of current and voltage allows you to use the familiar dc formulas, such as V = IR and P = I 2 R. One ac ampere is said to flow in a circuit if it produces the same joule heating as one ampere of dc current under the same conditions. At your house the peak voltage will be 170 V 11/13/2018

What is the rms value of an AC voltage whose maximum value is 141 V? QUIZ lecture 19 What is the rms value of an AC voltage whose maximum value is 141 V? zero 70.7 V 100 V 141 V 240 V 11/13/2018

Inductors in AC Circuits 900 Potential drop, VL(t), leads the current, I(t) by 900 11/13/2018

Relationship between Irms & Vrms 11/13/2018

Phasors for L V leads I by 90 90 degrees out of phase…..if I and V 90 out of phase no power loss 11/13/2018

Quiz Questions If we increase the driving frequency in a circuit with a purely inductive load does IL Decrease Increase Remain the Same VL remains the same IL decreases If we increase the driving frequency in a circuit with a purely inductive load does VL Decrease Increase Remain the Same 11/13/2018

Capacitors in AC Circuits 900 Potential drop, VC(t), lags the current, I(t), by 900 11/13/2018

Relationship between Irms & VC,rms 11/13/2018

Phasors for C V lags I by 90 Conventions….most important 90 degrees out of phase But capacitors and inductors are 180 out of phase with each other 11/13/2018

Summary Symbol Reactance X C L L R IC current leads VC IL current lags VL 11/13/2018

Impedances for L, C, R R is resistance is capacitive reactance For high , XC goes to zero, C acts like a wire. For low , XC grows larger and at DC, C acts like an open switch XL = L is inductive Reactance For high , XL grows large and L acts like an open switch. For low , XL grows small and at DC, L acts like a conducting wire. 11/13/2018

Phasors for R V in phase with I 11/13/2018

Phasors for C V lags I by 90 11/13/2018

Phasors for L V leads I by 90 11/13/2018

AC Power Distribution AC power can travel at high voltages and low amps, therefore smaller power loss Tesla liked 60 Hz and 240 V Standard in Europe was defined by a German company AEG ( monopoly) who chose 50Hz (20% less efficient in generation, 10-15% less efficient in transmission) Originally Europe was also 110V, but they changed to reduce power loss and voltage drop for the same copper diameter Nikola Tesla http://www.teslasociety.com/ 11/13/2018

The Power Grid 11/13/2018

Example If 735 kV line is used to transmit electric energy 1000 km. I = 500 A and R = 0.220 W/km Energy is supplied at a rate of Energy dissipated from resistance of wires If you doubled the current and halved the voltage, energy dissipated 11/13/2018

LC Circuits ++++ - - - - R C L C ++++ - - - - Consider the LC and RC series circuits shown: Suppose that at t=0 the capacitor is charged to a value of Q. Is there is a qualitative difference in the time development of the currents produced in these two cases. Why?? 11/13/2018

LC Oscillations L C I ++++ - - - - Kirchoff’s loop rule 11/13/2018

LC Oscillations Q V C I V t L dI dt t 11/13/2018

Example 1 (a) Vab < 0 (b) Vab = 0 (c) Vab > 0 L C t=0 L C t=t1 + - Q Qo = L C t=t1 Q = At t=0, the capacitor in the LC circuit shown has a total charge Q0. At t = t1, the capacitor is uncharged. What is the value of Vab, the voltage across the inductor at time t1? (a) Vab < 0 (b) Vab = 0 (c) Vab > 0 11/13/2018

Example 2 (a) I2 = I0 (b) I2 = 2I0 (c) I2 = 4I0 t=0 + - Q Qo = At t=0 the capacitor has charge Q0; the resulting oscillations have frequency 0. The maximum current in the circuit during these oscillations has value I0. What is the relation between I0 and I2 , the maximum current in the circuit when the initial charge = 2Q0? (a) I2 = I0 (b) I2 = 2I0 (c) I2 = 4I0 11/13/2018

Example 3 (a) 2 = 1/2 0 (b) 2 = 0 (c) 2 = 20 t=0 + - Q Qo = At t=0 the capacitor has charge Q0; the resulting oscillations have frequency 0. The maximum current in the circuit during these oscillations has value I0. What is the relation between 0 and 2, the frequency of oscillations when the initial charge = 2Q0? (a) 2 = 1/2 0 (b) 2 = 0 (c) 2 = 20 11/13/2018