Rank the magnitude of current induced into a loop by a time-dependent current in a straight wire. I(t) A B C D E tI(t)I induced

What is the direction of the induced current in the loop? Zero counterclockwise clockwise Some other direction

What is the direction of the induced current in the loop? Zero counterclockwise clockwise Some other direction S N

When the switch is closed, the potential difference across R is… V N1 N2>N1 Zero R V N2/N1 V N1/N2 V

Once the switch is closed, the ammeter shows… V N1 N2>N1 A R Zero Current Steady Current Nonzero Current for a short time

A transformer is fed the voltage signal V p (t). What is the secondary voltage signal? V p (t) t

The concept of self-inductance resembles … Aging; the older you get, the weaker you get Being taxed; the more money you make, the more taxes you pay Swimming; the more you press the water away, the harder the water presses back Baron Muenchausen; he pulled himself out of the swamps by his own hair

Self-inductance L is analogous to … Electric charge Potential energy (Inertial) mass Momentum (Hint: it has to be a property of an object)

Given are the potential energies U as a function of the current I of several inductors. Which has the smallest self- induction L? U I U U U I I I

A Solenoid produces a changing magnetic field that induces an emf which lights bulbs A & B. After a short is inserted, … A goes out, B brighter B goes out, A brighter A goes out, B dimmer B goes out, A dimmer x x x A x x B

A straight wire carries a constant current I. The rectangular loop is pushed towards the straight wire. The induced current in the loop is … Zero Clockwise I Counter-clockwise Need more information

When the switch is closed in an LR circuit, the current exponentially reaches the maximal value I=V/R. The time constant is τ =L/R. After which time does the current reach half its maximal value? Immediately After 1 time constant (t = τ) After 2 time constants (t = 2 τ) After about 70% of a time constant (t = 0.69 τ )

When the switch is closed in an LR circuit, the current exponentially reaches the maximal value I=V/R. If the inductor (a solenoid, say), is replaced by a solenoid with twice the number of windings, the time the current takes to reach half its maximal value …? does not change is halved doubles quadruples

The current in an LC circuit will oscillate with a frequency f. To change the frequency we can… … change the initial charge of the capacitor … change the inductance of the inductor …do nothing. It is fixed by the physics of LC circuits.

The current in an LC circuit will oscillate with a frequency f. If we replace the capacitor by one with twice its capacitance, the frequency … doubles quadruples is halved None of the above.

The current in an LC circuit will oscillate with a frequency f. If we add a small resistance to the circuit, … the frequency goes up the amplitude goes down the current decays exponentially Two of the above

Assume a sinusoidal current: I=I 0 sinω t. In an AC circuit with a resistor R, which diagram describes the voltage across the resistor correctly? V t V V V t t t

Assume a sinusoidal current: I=I 0 sinω t. In an AC circuit with an inductor L, which diagram describes the voltage across the inductor correctly? V t V V V t t t

Assume a sinusoidal current: I=I 0 sinω t. In an AC circuit with an capacitor C, which diagram describes the voltage across the capacitor correctly? V t V V V t t t

Resistor

Inductor Potential difference (voltage) gets current flowing Induction slows current down  Voltage first!

Capacitor Flow of charges (current) builds up electric field (voltage)  Current first!

LRC circuit with AC driving emf Voltages different: V R, V L, V C Common to all: current  Use current as reference

Phasors Phasors turn with angular frequency ω Direction is position within cycle Length of phasor is peak value of V, I, Z Value is projection on y axis E.g.: V C =0, V R =V R0

A little later … ALL phasors have turned by an angle ωt Angles between phasors are preserved ALL values of V, I have changed E.g.: V L (t=later) = V L0 sin (ωt+π/2)

Projections on x-axis are values at time t

Adding Phasors Add like vectors Phase angle will be between 90 and -90

Assume a sinusoidal current: I=I 0 sin(2πf t). In a resistor circuit with frequency 2 Hz, which phasor diagram describes the voltage across the resistor at t = 1.5 s if the phase at t=0 was zero?

Assume a sinusoidal current: I=I 0 sinω t. In an AC circuit with a capacitor C, which phasor diagram describes the voltage across the capacitor correctly?

Assume a sinusoidal current: I=I 0 sinω t. In an AC circuit with a inductor I, which phasor diagram describes the voltage across the inductor correctly?

Assume a sinusoidal current: I=I 0 sin(2πf t). What can you tell from the phasor diagram below about an LRC ac circuit if the orange arrow represents the instantaneous voltage across the whole circuit? The frequency is 1/8 Hz The phase angle of the current is about 30 degrees The inductive reactance is smaller than the capacitive reactance The resistance is very small

Assume a sinusoidal current: I=I 0 sin(2πf t). Which of the following is true about an LRC ac circuit? The phase angle between current and voltage constant The voltage is constant The power consumed by the circuit is zero The power consumed by the circuit is constant

Group Work on AC LRC circuits L=200mH, R=1000 Ohm, C = 60μF, driven by a 30V power supply at 1kHz. Draw the voltages and the current in a phasor diagram at t=1/4000 s. Calculate the reactances Calculate the impedance of the circuit Find the phase angle What is the (average) power used by the circuit?

In Physlet I 31.7 an RC circuit is animated. What happens if the frequency increases? Nothing except the voltage phasor rotating faster The reactance of the capacitor goes up and hence the phase angle between voltage and current changes All reactances (R, C) change The reactance of the inductor goes up, of the capacitor goes down, and the voltage phasor rotates faster

In Physlet I 31.7 an RC circuit is animated. What will happen if the frequency is halved? The reactance of the resistor halves The reactance of the capacitor doubles The peak voltage across the source changes The phase angle between the voltage across R and the voltage across C changes

In Physlet I 31.7 an RC circuit is animated. What will happen if the frequency is halved? The voltage across the resistor halves The voltage across the capacitor doubles The peak voltage across the source changes None of the above

Why does the voltage across the capacitor not double if the frequency is halved? The reactance of the capacitor does not double The current through the circuit drops The peak voltage across the source does not change The phase angle between the voltages does not change enough

Consider a LRC circuit which at f = 1kHz displays R=X C =X L =1000Ω. At 10 kHz we have … R=X C =X L =1000Ω R=1000Ω, X C > X L =10000Ω R = X C = X L =10000Ω R=1000Ω, X C =100Ω < X L

Consider a LRC circuit which at f = 1kHz displays R=X C =X L =1000Ω. At 10 Hz we have … R=X C =X L =1Ω R=1000Ω, X C > X L =1Ω R = X C = X L =1MΩ R=1000Ω, X C =100Ω < X L

In Physlet I 31.8 the impedance Z of a LRC circuit is plotted. What happens if the value for R is chosen very big? Plot changes, but remains qualitatively the same Nothing changes The curve is shifted up The curve becomes flat

The impedance of a LRC circuit depends on the frequency. What is special about the frequency where capacitor and the inductor have the same reactance? Nothing Impedance has a minimum Current is at a minimum All voltages are in phase

As one of Maxwell’s equations, Gauss’s Law is … Homogeneous and concerning the electric field Inhomogeneous and concerning the electric field Homogeneous and concerning the magnetic field Inhomogeneous and concerning the magnetic field

As one of Maxwell’s equations, (modified) Ampere’s Law is … Homogeneous and concerning the electric field Inhomogeneous and concerning the electric field Homogeneous and concerning the magnetic field Inhomogeneous and concerning the magnetic field

As one of Maxwell’s equations, magnetic Gauss’s Law is … Homogeneous and concerning the electric field Inhomogeneous and concerning the electric field Homogeneous and concerning the magnetic field Inhomogeneous and concerning the magnetic field

As one of Maxwell’s equations, Faraday’s Law is … Homogeneous and concerning the electric field Inhomogeneous and concerning the electric field Homogeneous and concerning the magnetic field Inhomogeneous and concerning the magnetic field

Electromagnetic Waves Medium = electric and magnetic field Speed = 3  10 5 km/sec

Production of EM waves Current flowing creates B field Charges accumulating create E field

EM Waves radiating out As the direction of the current changes, the “second half” of the wave is created  E, B in opposite direction as in first half, but in same direction as in “back part” of first half

Wave travels in empty space

Directions of E, B are perpendicular but in phase E, B are perpendicular to direction of motion of wave  transverse wave

The EM spectrum

Receiving an EM Wave