Concept Questions Calculate flux downwards – we get EMF clockwise Flux is decreasing Derivative of flux is negative EMF is positive clockwise Current will flow clockwise 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) ClockwiseB) Counter-clockwiseC) No current D) Insufficient information The current that flows will then create a magnetic field, which inside the loop, will A) Strengthen itB) Weaken it C) No changeD) Insufficient information Right hand rule – B-field downwards Reinforces magnetic field Tries to keep the B-flux constant

Concept Question 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 What happens as I drop the magnet into the copper tube? A) Falls as usualB) Falls slower C) Falls fasterD) Floats constant E) Pops back up and out 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 N S S N S N What if we used a superconductor?

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

Concept Question L E = 12 V + – In the steady state, with the switch closed, how much current flows through R 2 ? How much current flows through R 2 the moment after we open the switch? A) 0 AB) 6 AC) 3 A D) 2 AE) None of the above R 1 = 2  In the steady state, the inductor is like a wire Both ends of R 2 are at the same potential: no current through R 2 The remaining structure had current I = E /R 1 = 6 A running through it 6 A I = 6 A R 2 = 4  Now open the switch – what happens? Inductors resist changes in current, so the current instantaneously is unchanged in inductor It must pass through R 2 I = E /R 1 = 6 A 6 A

L E = 10 V + – The circuit at right is in a steady state. What will the voltmeter read as soon as the switch is opened? A) 0.l VB) 1 VC) 10 V D) 100 VE) 1000 V R 1 = 10  The current remains constant at 1 A It must pass through resistor R 2 The voltage is given by  V = IR R 2 = 1  k  Note that inductors can produce very high voltages Inductance causes sparks to jump when you turn a switch off I = 1 A + – Loop has unin- tended inductance V Concept Question

A capacitor with charge on it has energy U = Q 2 /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! Concept Question C L Q I Energy sloshes back and forth Let’s find the energy in the capacitor and the inductor

If the voltage from a source looks like the graph below, about what voltage should it be labeled? A)0 VB) 170 VC) 120 VD) 85 V E) It should be labeled some other way Concept Question 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

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

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: (A)Let low frequencies through, but block high frequencies (B)Let high frequencies through, but block low frequencies (C)Let small currents through, but not big currents (D)Let big currents through, but not small currents

Impedance Table ResistorCapacitorInductor ImpedanceR Phase0 Vector Direction rightdownup Inductors are good for (A)Blocking low frequencies (B)Blocking high frequencies (C)Blocking large currents (D)Blocking small currents

Concept Question 1.4 k  2.0  F 60 Hz 170 V ? 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 capacitorB) The inductorC) both D) Insufficient information L= 4.0 H 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 1.4 k  1.5 k  1.3 k 

Concept Question R C f V max L How will X L and X C compare at the frequency where the maximum power is delivered to the resistor? A) X L > X C B) X L < X C C) X L = X C D) Insufficient information Resonance happens when X L = X C. This makes Z the smallest It happens only at one frequency Same frequency we got for LC circuit

Concept Question R C L In the example we just did, we found only some frequencies get through f V max = 5 V 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

Concept Question 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 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 Voltage Current

Concept Question N 1 =5000 N 2 =?  V 1 = 10 kV  V 2 = 120 V 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) 120B) 240C) 60 D) None of the above

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 B 0 = E 0 / 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 +i direction 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 Concept Question

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 Increasing f Increasing Red Orange Yellow Green Blue Violet

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)  a 2  S  /cB) 2  a 2  S  /cC) 4  a 2  S  /c As viewed from any side, a sphere looks like a circle of radius a The cross section for a sphere, then, is  a 2

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