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Alternating Current (AC)

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

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Alternating Current (AC)

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  1. where Alternating Current (AC) = Electric current that changes direction periodically ac generatoris a device which creates an ac emf/current. A sinusoidally oscillating EMF is induced in a loop of wire that rotates in a uniform magnetic field. ac motor = ac generator run in reverse http://www.wvic.com/how-gen-works.htm http://www.pbs.org/wgbh/amex/edison/sfeature/acdc.html

  2. Similarly, Root-Mean-Square Values

  3. I(t) leads v(t) by 90 capacitive reactance vL(t) leads I(t) by 90 -- + inductive reactance Capacitive vs Inductive Load -- + vL

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

  5. Mechanical Analogy No friction = No dissipation harmonic oscillator with

  6. LC Oscillations No Resistance = No dissipation

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

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

  9. Finite R Energy dissipation damped oscillation only if R is “small” For large R multiply by I 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.

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

  11. Voltage and Current in Driven Series RLC Circuit Phasors

  12. impedance,   Impedance in Driven Series RLC Circuit

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

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

  15. Power factor Power Delivered

  16. step-up step-down 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) With resistive load R in secondary, current I2 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 I1 which is induced on the primary side due to I2.

  17. With switch S closed: Imag+I1 I2 S conservation of energy proportional to average power equivalent resistance Req The generator “sees” a resistance of Req 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. Transformer with a Load

  18. 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? • Double L • Double both L and C • Halve L • Halve both L and C • Double L and halve C

  19. 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? • Double C • Double both L and C • Halve C • Halve both L and C • Double L and halve C

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