Electromagnetic Oscillations and Alternating Current

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Presentation transcript:

Electromagnetic Oscillations and Alternating Current Chapter 31 Electromagnetic Oscillations and Alternating Current In this chapter we will cover the following topics: -Electromagnetic oscillations in an LC circuit -Alternating current (AC) circuits with capacitors -Resonance in RCL circuits -Power in AC-circuits -Transformers, AC power transmission (31 - 1) Induction - Spring 2006

LR Circuit i Steady Source Induction - Spring 2006

Max Current Rate of increase = max emf VR=iR ~current Induction - Spring 2006

Solve the loop equation. Induction - Spring 2006

Time Dependent Result: Induction - Spring 2006

We also showed that Induction - Spring 2006

At t=0, the charged capacitor is now connected to the inductor At t=0, the charged capacitor is now connected to the inductor. What would you expect to happen?? Induction - Spring 2006

L C (31 - 2) Induction - Spring 2006

L C (31 - 3) Induction - Spring 2006

L C (31 - 4) Induction - Spring 2006

The Graph of that LC (no emf) circuit .. Induction - Spring 2006

Induction - Spring 2006

Mass on a Spring Result Energy will swap back and forth. Add friction Oscillation will slow down Not a perfect analogy Induction - Spring 2006

Induction - Spring 2006

LC Circuit High Q/C Low Low High Induction - Spring 2006

The Math Solution (R=0): Induction - Spring 2006

New Feature of Circuits with L and C These circuits produce oscillations in the currents and voltages Without a resistance, the oscillations would continue in an un-driven circuit. With resistance, the current would eventually die out. Induction - Spring 2006

Variable Emf Applied emf DC Sinusoidal Induction - Spring 2006

Sinusoidal Stuff “Angle” Phase Angle Induction - Spring 2006

Same Frequency with PHASE SHIFT f Induction - Spring 2006

Different Frequencies Induction - Spring 2006

Induction - Spring 2006 (31 - 6)

Induction - Spring 2006 (31 - 7)

Note – Power is delivered to our homes as an oscillating source (AC) This makes AC Important! Induction - Spring 2006

Producing AC Generator x x x x x x x x x x x x x x x x x x x x x x x Induction - Spring 2006

The Real World Induction - Spring 2006

A Induction - Spring 2006

Induction - Spring 2006

The Flux: Induction - Spring 2006

Source Voltage: Induction - Spring 2006

(31 - 10) Induction - Spring 2006

(31 - 12) Induction - Spring 2006

O (31 - 13) Induction - Spring 2006

(31 - 14) Induction - Spring 2006

O (31 - 15) Induction - Spring 2006

(31 - 16) Induction - Spring 2006

SUMMARY Circuit element Average Power Reactance Phase of current Voltage amplitude Resistor R Current is in phase with the voltage Capacitor C Current leads voltage by a quarter of a period Inductor L Current lags behind voltage by a quarter of a period (31 - 17) Induction - Spring 2006

(31 - 18) Induction - Spring 2006

O A B (31 - 19) Induction - Spring 2006

O A B (31 - 20) Induction - Spring 2006

(31 - 21) Induction - Spring 2006

(31 - 22) Induction - Spring 2006

(31 - 23) Induction - Spring 2006

(31 - 25) Induction - Spring 2006

Induction - Spring 2006 (31 - 26)

Induction - Spring 2006 (31 - 27)

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