Lecture 20-1 Alternating Current (AC) = Electric current that changes direction periodically ac generator is a device which creates an ac emf/current. ac motor = ac generator run in reverse A sinusoidally oscillating EMF is induced in a loop of wire that rotates in a uniform magnetic field. where

Lecture 20-2 Root-Mean-Square Values Similarly,

Lecture Capacitive vs Inductive Load I(t) leads v(t) by 90  capacitive reactance v L (t) leads I(t) by 90  inductive reactance vLvL

Lecture 20-4 (Ideal) LC Circuit From Kirchhoff’s Loop Rule Natural Frequency harmonic oscillator with angular frequency

Lecture 20-5 Mechanical Analogy harmonic oscillator with No friction = No dissipation

Lecture 20-6 LC Oscillations No Resistance = No dissipation

Lecture 20-7 More on LC Oscillations Energy stored in capacitor: t 0 0 t Energy stored in inductor: where so Charge and current: (with  =0) Period is half that of Q(t)

Lecture 20-8 Non-scored Test Quiz A LC circuit has inductance L and capacitance C, what’s the natural frequency? A. B. C. D.

Lecture 20-9 Series RLC Circuits The resistance R may be a separate component in the circuit, or the resistance inherent in the inductor (or other parts of the circuit) may be represented by R. Finite REnergy dissipation damped oscillation only if R is “small” multiply by I For large R

Lecture Driven Series RLC Circuit Kirchhoff’s Loop Rule: common current I must be determined

Lecture Voltage and Current in Driven Series RLC Circuit  Phasors

Lecture  Impedance in Driven Series RLC Circuit impedance, 

Lecture Resonance For given  peak, R, L, and C, the current amplitude I peak will be at the maximum when the impedance Z is at the minimum. Resonance angular frequency: This is called resonance. i.e., load purely resistiveε and I in phase

Lecture Resonance (continued) angular frequency (radians/s): In a steady, driven RLC circuit, power dissipated = power supplied by ac source. This power is dissipated only in R. At resonance, this power is maximum. Power dissipated: frequency (Hz): Phase difference between ε and I: 

Lecture Power Delivered Power factor 

Lecture 20-16

Lecture Transformer AC voltage can be stepped up or down by using a transformer. AC current in the primary coil creates a time-varying magnetic flux through the secondary coil via the iron core. This induces EMF in the secondary circuit. Ideal transformer (no losses and magnetic flux per turn is the same on primary and secondary). (With no load) step-up step-down With resistive load R in secondary, current I 2 flows in secondary by the induced EMF. This then induces opposing EMF back in the primary. The latter EMF must somehow be exactly cancelled because  is a defined voltage source. This occurs by another current I 1 which is induced on the primary side due to I 2.

Lecture Transformer with a Load With switch S closed: conservation of energy proportional to average power S I mag +I 1 I2I2 equivalent resistance R eq The generator “sees” a resistance of R eq Impedance Matching: Maximum energy transfer occurs when impedance within the EMF source equals that of the load. Transformer can vary the “effective” impedance of the load.

Lecture Physics 241 –Quiz 17b – March 25, 2008 An LC circuit has a natural frequency of 141 MHz. If you want to decrease the natural frequency to 100 MHz, which of the following will accomplish that? a)Double L b)Double both L and C c)Halve L d)Halve both L and C e)Double L and halve C

Lecture Physics 241 –Quiz 17c – March 25, 2008 An LC circuit has a natural frequency of 100 MHz. If you want to decrease the natural frequency to 71 MHz, which of the following will accomplish that? a)Double C b)Double both L and C c)Halve C d)Halve both L and C e)Double L and halve C