Physics 132 Quiz # 23

Transcription

1 Name (please (please print) print) Physics 132 Quiz # 23 I. I. The The current in in an an ac ac circuit is is represented by by a phasor.the value of of the the current at at some time time t t is is given by by the the length of of the thephasor the the value, in in radians, of of the the angle between the the phasor and and the the horizontal axis. axis the the projection of of the thephasor on on one one of of the the axes. axes. II. II. A capacitor having an an initial charge Q is is connected in in series with with an an inductor and and a resistor. As As a function of of time, time, the the charge on on the the capacitor oscillates sinusoidally oscillates sinusoidally with with exponentially decreasing amplitude does does not not vary vary in in time time as as there there is is no no driving emf. emf not not covered in in the the reading assignment

2 LECTURE 26 Topics Phasors LC & RLC circuits (no source)

3 Phasors New Concept: Phasors --rotating vectors in in x-y plane --constant angular velocity ω A(t) A0 sin( ωt δ ) A 0 ωt δ A0 cos( ωt δ ) useful for illustrating phase difference between oscillating quantities (currents, voltages in AC circuits)

4 Concept Test: The The phasor diagrams represent three three oscillating emfs emfs having different amplitudes and and frequencies at at t=0. t=0. At At finite t t each each phasor rotates counterclockwise. At At the the instant t t shown, the the magnitude E(t) E(t) associated with with each each phasor given in in decreasing order is is E(t) a.) b.) c.) 1. a.), b.) and c.) 2. a.), c.) and b.) 3. b.), c.) and a.) 4. c.), a.), and b.) 5. none of the above 6. need more information

5 Concept Test: Consider the the pairs pairs of ofphasors below, each each shown at at t t = All All are are characterized by by a common frequency of of oscillation ω. ω. If If we we add add the the oscillations, the the maximum amplitude is is achieved for for pair pair

6 Concept Test: Consider the the oscillating emf emfshown below. Which of of the thephasor diagrams correspond(s) to to this this oscillation:

7 Example: voltage across resistor Fig.1 Fig. 2 Exercise: (a) (a) find the the phase difference δ between the the voltage and current signal shown in in Fig. 1, 1, (b) (b) draw the the current phasor on on Fig. 2

8 Exercise: draw the phasors for current and voltage corresponding to the signals shown

9 Mechanical analog LC circuit: electric oscillator di Q L + = dt C dq I = dt 2 d Q Q L + 2 dt C 0; = 0 Look for a solution of the following form: Q( t) = Q0 cos( ωt) Calculate ω: Calculate the current I(t)

10 LC circuit Q(t), I(t) draw graphs Q vs. t and I vs t t draw the phasors for Q(t) and I(t)v Calculate and plot the electric, magnetic and total energy as a function of time: U E (t), U B (t) t

11 Mechanical analog RLC circuit: damped oscillator di Q L + dt C dq I = dt 2 d Q L + 2 dt + IR Q C + R = 0; dq dt = 0 Look for a solution of the following form: Q( t) = Q e 0 ωt A.) underdamped B.) critically damped C.) overdamped oscillator Need a generator to to sustain oscillations