electricity and magnetism ii
DESCRIPTION
AC1. Electricity and Magnetism II. AC Circuits & Complex Numbers Clicker Questions. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/1.jpg)
Electricity and Magnetism II
AC Circuits & Complex NumbersClicker Questions
AC1
![Page 2: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/2.jpg)
Loop 1 sits in a uniform field B which is increasing in magnitude. Loop 2 has the SAME LENGTH OF WIRE looped (coiled) to make two (smaller) loops. (The 2 loops are connected appropriately, think of it as the start of a solenoid) How do the induced EMFs compare? HINT: Don’t answer too quickly, it requires some thinking!
A) EMF(1)=4 EMF(2) B) EMF(1) = 2 EMF(2)C) They are both the same. D) EMF(2)= 4 EMF(1) E) EMF(2) = 2 EMF(1)
B
12
AC2
![Page 3: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/3.jpg)
R
LV0
The switch is closed at t=0. What can you say about I(t=0+)?
IA) ZeroB) V0/RC) V0/LD) Something else!E) ???
AC3
![Page 4: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/4.jpg)
R
LV0
The switch is closed at t=0. Which graph best shows I(t)?
E) None of these (they all have a serious error!)
t
t
t
t
I
I
I
I
I
AB
C
D
AC4
![Page 5: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/5.jpg)
Consider a cubic meter box of uniform magnetic field of 1 Tesla and a cubic meter box of uniform electric field of 1 Volt/meter. Which box contains the most energy?
A. The box of magnetic fieldB. The box of electric fieldC. They are both the sameD. Not enough information given
AC5
![Page 6: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/6.jpg)
R
LV0
The switch is closed at t=0. What can you say about the magnitude of ΔV(across the inductor) at (t=0+)? I
A) ZeroB) V0
C) LD) Something else!E) ???
AC6
![Page 7: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/7.jpg)
A) a=AcosφB) a=AsinφC) I can do this, but it’s more complicated than either of the above!D) I’m not sure at the moment how to do this. E) It’s a trick, these two forms are not equivalent!
The solution to an ODE isI(t) = a cos(ωt) + bsin(ωt), (with a and b still undetermined constants) Or equivalently, I(t) = A cos(ωt+φ) (with A and φ still undetermined constants) Which expression connects the constants in these two forms?
AC7
![Page 8: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/8.jpg)
A) A=a2+b2
B) A=Sqrt[a2+b2]C) I can do this, but it’s more complicated than either of the above!D) I’m not sure at the moment how to do this.
The solution to an ODE isI(t) = a cos(ωt) + bsin(ωt), (with a and b still undetermined constants) Or equivalently, I(t) = A cos(ωt+φ) (with A and φ still undetermined constants) Which expression connects the constants in these two forms?
AC8
![Page 9: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/9.jpg)
The complex exponential: is useful in calculating properties of many time-dependent equations. According to Euler, we can also write this function as:A) cos(i ω t) + sin(i ω t) B) sin(ω t) + i cos(ω t)C) cos(ω t) + i sin(ω t) D) MORE than one of these is correctE) None of these is correct!
i te AC9
![Page 10: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/10.jpg)
What is |2+i|
A) 1B) Sqrt[3]C) 5D) Sqrt[5]E) Something else!
AC10
![Page 11: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/11.jpg)
11
Which point below best represents 4ei3π/4 on the complex plane?
Challenge question: Keeping the general form Aei θ, do any OTHER values of θ represent the SAME complex number as this? (If so, how many?)
A
B
C
D
E) Not sure and/ornone of these!!
Re
Im
AC11
![Page 12: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/12.jpg)
12
What is
A) ei π/4
B) Sqrt[2] ei π/4
C) ei 3π/4
D) Sqrt[2]ei 3π/4
E) Something else!There are two obvious methods. 1) multiply it out (“rationalizing” the denominator)Or 2) First write numerator and denominator in standard Aeiθ form.Both work. Try it with method 2b
AC12
![Page 13: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/13.jpg)
13
What is (1+i)2/(1-i)AC13
![Page 14: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/14.jpg)
14
What is (1+i)2/(1-i)AC14
![Page 15: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/15.jpg)
15
What is (1+i)2/(1-i)AC15
![Page 16: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/16.jpg)
16
What is (1+i)2/(1-i)AC16
![Page 17: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/17.jpg)
AC voltage V and current I vs time t are as shown:
tV I
A) I leads V ( I peaks before V peaks )
B) I lags V ( I peaks after V peaks )
C) Neither
The graph shows that..
I leads V = I peaks before V peaksI lags V = I peaks after V peaks
AC17
![Page 18: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/18.jpg)
R
LV
I
Suppose
are complex solutions of this equation:
ˆd Iˆ ˆV I R Ld t
j t0
ˆ ˆV V e and I
Is it always true that the real parts of these complex variables are solutions of the equation?
A) Yes, always B) No, not always
AC18
![Page 19: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/19.jpg)
i i0 00
V VI e ei L L
The phase angle δ =
A) 0
B) +π/2
C) –π/2
D) +π
E) –π
AC19
![Page 20: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/20.jpg)
j / 2V I Z I Z e j / 2V VI e
Z Z
Re
Im
V = Voejt
t
AB
CD
E)None of these
Which is the correct current phasor?
AC20
![Page 21: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/21.jpg)
R
L
C
V
I
What is the total impedance of this circuit?
Ztotal =
1 1A) R j L B) R j LC C
1 1 1C) j C D)1 1R j L j CR j L
E) None of these
AC21
![Page 22: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/22.jpg)
What is
AC22
![Page 23: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/23.jpg)
Suppose you have a circuit driven by a voltage
V(t)=V0cos(ωt), and you observe the resulting current is I(t) = I0cos(ωt-π/4).
Would you say the current isA) leadingB) laggingthe voltage by 45 degrees?
AC23
![Page 24: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/24.jpg)
A simple RC circuit is driven by an AC power supply with an emf described by
A. 0B. V0
C. -V0 D. Not enough information given
The voltage across the capacitor (Va – Vb) just after t=0 is
a
b
AC24
![Page 25: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/25.jpg)
A simple RC circuit is driven by an AC power supply with an emf described by
A. 0B. V0/RC. -V0/RD. Not enough information given
The current through the capacitor just after t=0 is
+I
AC25
![Page 26: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/26.jpg)
Given a capacitance, C, and a resistance, R, the units of the product, RC, are:
A) AmpsB) Volts*secondsC) secondsD) 1/seconds.E) I do know the answer, but can’t prove it in the 60
seconds I’m being given here...
AC26
![Page 27: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/27.jpg)
The ac impedance of a RESISTOR is:
A) Dependent on voltage drop across the resistor.B) Dependent on current flowing into the resistor.C) Both A) and B)D) None of the above.E) ???
AC27
![Page 28: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/28.jpg)
The ac impedance of a capacitor is:
A) Dependent on the magnitude of the voltage drop across the capacitor.
B) Dependent on the magnitude of the current flowing into the capacitor.
C) Both A) and B)D) None of the above.E) ??
AC28
![Page 29: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/29.jpg)
The ac impedance of an inductor is:
A) Dependent on voltage drop across and/or current through the inductor.
B) .C) .D) None of the above.
ZL i LZ 1L i L
AC29
![Page 30: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/30.jpg)
R
LV0
Two LR circuits driven by an AC power supply are shown below.
A. The left circuit B) The right circuit C) Both circuitsD) Neither circuit E) ???
Which circuit is a low pass filter?(“Low pass” means low freq. inputs yield strong output, but high frequency input is “blocked”, you get no output. So “low pass” filters reduce high frequencies, and passes the low frequencies…)
R
L
V0
AC30
![Page 31: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/31.jpg)
Two RC circuits driven by an AC power supply are shown below.
A. The left circuitB. The right circuitC. Both circuitsD. Neither circuitE. Not enough information given
Which circuit is a high pass filter?
AC31
![Page 32: Electricity and Magnetism II](https://reader036.vdocument.in/reader036/viewer/2022062410/568161bb550346895dd192f5/html5/thumbnails/32.jpg)
Two RC circuits driven by an AC power supply are shown below.
A. The left circuitB. The right circuitC. Both circuitsD. Neither circuit
Which circuit is a high pass filter?
AC32