Electricity and Magnetism II

1. AC1 Electricity and Magnetism II AC Circuits & Complex Numbers Clicker Questions

2. 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! AC2 2 1 B 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)

3. AC3 The switch is closed at t=0. What can you say about I(t=0+)? Zero V0/R V0/L Something else! ??? I R V0 L

4. AC4 The switch is closed at t=0. Which graph best shows I(t)? E) None of these (they all have a serious error!) I R A I B V0 L I t t D t I C I t

5. 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? AC5 • The box of magnetic field • The box of electric field • They are both the same • Not enough information given

6. AC6 The switch is closed at t=0. What can you say about the magnitude of ΔV(across the inductor) at (t=0+)? I Zero V0 L Something else! ??? R V0 L

7. AC7 The solution to an ODE is I(t) = a cos(ωt) + bsin(ωt), (with a and b still undetermined constants) Or equivalently, I(t) = A cos(ωt+φ) (with A and φstill undetermined constants) Which expression connects the constants in these two forms? a=Acosφ a=Asinφ I can do this, but it’s more complicated than either of the above! I’m not sure at the moment how to do this. It’s a trick, these two forms are not equivalent!

8. AC8 The solution to an ODE is I(t) = a cos(ωt) + bsin(ωt), (with a and b still undetermined constants) Or equivalently, I(t) = A cos(ωt+φ) (with A and φstill undetermined constants) Which expression connects the constants in these two forms? A=a2+b2 A=Sqrt[a2+b2] I can do this, but it’s more complicated than either of the above! I’m not sure at the moment how to do this.

9. AC9 The complex exponential: is useful in calculating properties of many time-dependent equations. According to Euler, we can also write this function as: cos(iω t) + sin(iω t) sin(ωt) + icos(ω t) cos(ω t) + i sin(ω t) MORE than one of these is correct None of these is correct!

10. AC10 What is |2+i|A) 1B) Sqrt[3]C) 5D) Sqrt[5]E) Something else!

11. AC11 Which point below best represents 4ei3π/4 on the complex plane? Im D A C Re B Not sure and/ornone of these!! 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?)

12. AC12 What is • ei π/4 • Sqrt[2] ei π/4 • ei 3π/4 • Sqrt[2]ei 3π/4 • 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

13. AC13 What is (1+i)2/(1-i)

14. AC14 What is (1+i)2/(1-i)

15. AC15 What is (1+i)2/(1-i)

16. AC16 What is (1+i)2/(1-i)

17. AC17 AC voltage V and current I vs time t are as shown: V I t The graph shows that.. I leads V ( I peaks before V peaks ) I lags V ( I peaks after V peaks ) Neither I leads V = I peaks before V peaks I lags V = I peaks after V peaks

18. AC18 I Suppose are complex solutions of this equation: R V L Is it always true that the real parts of these complex variables are solutions of the equation? A) Yes, always B) No, not always

19. AC19 The phase angle δ = 0 +π/2 –π/2 +π –π

20. AC20 Im Which is the correct current phasor? V = Voejwt A B wt Re D C E)None of these

21. AC21 I What is the total impedance of this circuit? Ztotal = R V L C

22. AC22 What is

23. AC23 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?

24. A simple RC circuit is driven by an AC power supply with an emf described by AC24 a b The voltage across the capacitor (Va – Vb) just after t=0 is • 0 • V0 • -V0 • Not enough information given

25. A simple RC circuit is driven by an AC power supply with an emf described by AC25 +I The current through the capacitor just after t=0 is • 0 • V0/R • -V0/R • Not enough information given

26. AC26 Given a capacitance, C, and a resistance, R, the units of the product, RC, are: Amps Volts*seconds seconds 1/seconds. I do know the answer, but can’t prove it in the 60 seconds I’m being given here...

27. AC27 The ac impedance of a RESISTOR is: Dependent on voltage drop across the resistor. Dependent on current flowing into the resistor. Both A) and B) None of the above. ???

28. AC28 The ac impedance of a capacitor is: Dependent on the magnitude of the voltage drop across the capacitor. Dependent on the magnitude of the current flowing into the capacitor. Both A) and B) None of the above. ??

29. AC29 The ac impedance of an inductor is: Dependent on voltage drop across and/or current through the inductor. . . None of the above.

30. AC30 Two LR circuits driven by an AC power supply are shown below. R L V0 L V0 R 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…) • The left circuit B) The right circuit C) Both circuits • D) Neither circuit E) ???

31. Two RC circuits driven by an AC power supply are shown below. AC31 Which circuit is a high pass filter? • The left circuit • The right circuit • Both circuits • Neither circuit • Not enough information given

32. Two RC circuits driven by an AC power supply are shown below. AC32 Which circuit is a high pass filter? • The left circuit • The right circuit • Both circuits • Neither circuit