Concept Questions

1. Concept Questions A wire, initially carrying no current, has a radius that starts decreasing at t = 0. As it shrinks, which way does current begin to flow in the loop? A) Clockwise B) Counter-clockwise C) No current D) Insufficient information • Calculate flux downwards – we get EMF clockwise • Flux is decreasing • Derivative of flux is negative • EMF is positive clockwise • Current will flow clockwise • Right hand rule – B-field downwards • Reinforces magnetic field • Tries to keep the B-flux constant The current that flows will then create a magnetic field, which inside the loop, will A) Strengthen it B) Weaken itC) No changeD) Insufficient information

2. Concept Question S N N S S N What happens as I drop the magnet into the copper tube? A) Falls as usual B) Falls slower C) Falls faster D) Floats constant E) Pops back up and out • As magnet falls, some places have magnetic fields that diminish • Current appears, replacing magnetic field • This acts like a magnet, pulling it back up • At bottom end, current appears to oppose change • This repels the magnet, slowing it down • Current is only caused by motion of magnet • If motion stops, resistance stops current • If motion is small, opposition will be small • It doesn’t stop, it goes slowly What if we used a superconductor?

3. Concept Question I L + – E What is Kirchoff’s law for the loop shown? A) E+ L (dI /dt) = 0 B) E– L (dI /dt) = 0 C) None of the above D) I don’t know Kirchoff’s law for switches • The voltage change for an inductor is L (dI/dt) • Negative if with the current • Positive if against the current

4. Concept Question 6 A 6 A R2 = 4  6 A – + In the steady state, with the switch closed, how much current flows through R2? How much current flows through R2 the moment after we open the switch? A) 0 A B) 6 A C) 3 A D) 2 A E) None of the above L R1 = 2  E = 12 V • In the steady state, the inductor is like a wire • Both ends of R2 are at the same potential: no current through R2 • The remaining structure had current I = E/R1 = 6 A running through it I = E /R1 = 6 A • Now open the switch – what happens? • Inductors resist changes in current, so the current instantaneously is unchanged in inductor • It must pass through R2 I = 6 A

5. Concept Question – + – + The circuit at right is in a steady state. What will the voltmeter read as soon as the switch is opened? A) 0.l V B) 1 V C) 10 V D) 100 V E) 1000 V R1 = 10  L I = 1 A V R2 = 1 k E = 10 V • The current remains constant at 1 A • It must pass through resistor R2 • The voltage is given by V = IR • Note that inductors can produce very high voltages • Inductance causes sparks to jump when you turn a switch off Loop has unin-tended inductance

6. Concept Question I A capacitor with charge on it has energy U = Q2/2C, but Q is constantly changing. Where does the energy go? A) It is lost in the resistance of the wire B) It is stored as kinetic energy of the electrons C) It is stored in the inductor D) Hollywood! Q C L • Let’s find the energy in the capacitor and the inductor Energy sloshes back and forth

7. Concept Question • If the voltage from a source looks like the graph below, about what voltage should it be labeled? • 0 V B) 170 V C) 120 V D) 85 V • E) It should be labeled some other way • Average voltage is zero, but that doesn’t tell us anything • Maximum voltage 170 V is an overstatement • Power is usually proportional to voltage squared

8. Concept Question A 60 W light bulb is plugged into a standard outlet (Vrms = 120 V). What is the resistance of the bulb? A) 15  B) 30  C) 60  D) 120  E) 240 

9. Capacitors and Resistors Combined • Capacitors and resistors both limit the current – they both have impedance • Resistors: same impedance at all frequencies • Capacitors: more impedance at low frequencies Concept Question The circuit at right might be designed to: • Let low frequencies through, but block high frequencies • Let high frequencies through, but block low frequencies • Let small currents through, but not big currents • Let big currents through, but not small currents

10. Impedance Table Inductors are good for • Blocking low frequencies • Blocking high frequencies • Blocking large currents • Blocking small currents

11. Concept Question In the mystery box at right, we can put a 2.0 F capacitor, a 4.0 H inductor, or both (in series). Which one will cause the greatest current to flow through the circuit? A) The capacitor B) The inductor C) both D) Insufficient information 1.4 k ? 60 Hz170 V 2.0 F • We want to minimize impedance • Make the vector sum as short as possible • Recall, capacitors point down, inductors up • The sum is shorter than either separately L= 4.0 H 1.3 k 1.5 k 1.4 k

12. Concept Question L C R f Vmax How will XL and XC compare at the frequency where the maximum power is delivered to the resistor? A) XL > XCB) XL< XCC) XL = XCD) Insufficient information • Resonance happens when XL = XC. • This makes Z the smallest • It happens only at one frequency • Same frequency we got for LC circuit

13. Concept Question • In the example we just did, we found only some frequencies get through What happens if this is impossible to meet, because 1/RC > R/L? A) The inequality gets reversed, R/L <  <1/RC B) Pretty much everything gets blocked C) Only a very narrow frequency range gets through C L R f Vmax = 5 V

14. Concept Question Voltage When the voltage shown in blue was passed through two components in series, the current shown in red resulted. What two components might they be? A) Capacitor and Inductor B) Inductor and Resistor C) Capacitor and Resistor Current • The phase shift represents how the timing of the current compares to the timing of the voltage • When it is positive, the current lags the voltage • It rises/falls/peaks later • When it is negative, the current leads the voltage • It rises/falls/peaks earlier

15. Concept Question N1 =5000 N2 =? V2 = 120 V V1 = 10 kV A transformer has 10,000 V AC going into it, and it is supposed to produce 120 V AC, suitable for household use. If the primary winding has 5,000 turns, how many should the secondary have? A) 120 B) 240 C) 60 D) None of the above

16. Concept Question • A wave has an electric field given by • What does the magnetic field look like? • A) B) • C) D) • The magnitude of the wave is B0 = E0 / c • The wave is traveling in the z-direction, because of sin(kz - t). • The wave must be perpendicular to the E-field, so perpendicular to j • The wave must be perpendicular to direction of motion, to k • It must be in either +idirection or –i direction • If in +i direction, then E  B would be in direction j  i = - k, wrong • So it had better be in the –i direction

17. Concept Question f Increasing  Increasing Which of the following waves has the highest speed in vacuum? A) Infrared B) Orange C) Green D) It’s a tie E) Not enough info Radio Waves Microwaves Infrared Visible Ultraviolet X-rays Gamma Rays Red Orange Yellow Green Blue Violet

18. Cross-Section • To calculate the power falling on an object, all that matters is the light that hits it • Example, a rectangle parallel to the light feels no pressure • Ask yourself: what area does the light see? • This is called the cross section If light of intensity S hits an absorbing sphere of radius a, what is the force on that sphere? A) a2S/c B) 2a2S/c C) 4a2S/c • As viewed from any side, a sphere looks like a circle of radius a • The cross section for a sphere, then, is a2

19. Equations for Test 3 Faraday’s Law Transformers: Power and Pressure Impedance: Inductors: Units: Frequency, Wavelength Speed of Light End of material for Test 3