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Understanding Electrical Circuits: Eddy Currents, Lenz Law, and Energy Transfer

Explore the principles of electromagnetic induction, Lenz's law, and the conservation of energy in electrical circuits. Learn about eddy currents, counter torque, self-inductance, and energy storage in capacitors and inductors. Understand the behavior of current and voltage in AC circuits.

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Understanding Electrical Circuits: Eddy Currents, Lenz Law, and Energy Transfer

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  1. Moving conductor – eddy currents • A increases  F increases  Induced current creates Bint opposite to external Bext • I down • Now we have a current in magnetic field  there is a force acting on it • The direction of this force is opposite to v • Conservatism of nature • Currents created in conductors moving through the magnetic field – eddy currents – work to resist the change Lecture XVIII

  2. Electric generator –counter torque • Loop is rotating cw • Induced currents experience force in magnetic field  resultant torque on the loop ccw – counter torque • Nature resists change. Lecture XVIII

  3. Electric motor – counter emf • Current loop in magnetic field • Magnetic field creates a torque that rotates the loop • Changing flux  emf • Based on conservatism – this emf will try to create a current in the opposite direction to the original current - counter emf. • Current is large at the beginning and is decreased later on. Lecture XVIII

  4. AC circuits Physics 122 Lecture XVIII

  5. Math review • Integrals and derivatives of trig. functions: • Relations between trig functions: Lecture XVIII

  6. Self inductance • Magnetic field in a solenoid • It creates a magnetic flux through itself • Self inductance of a solenoid In general: Lecture XVIII

  7. Direction of induced emf • In accordance to Lenz law • I – increase F increase  induced magnetic field in the opposite direction to initial magnetic field  emf in the opposite direction to original emf • I – decrease F decrease  induced magnetic field in the same direction to initial magnetic field  emf in the same direction to original emf Lecture XVIII

  8. Current and voltage in AC circuit Drop of voltageover resistor (V) follows I Current and voltagein phase Lecture XVIII

  9. Current and voltage in AC circuit • I goes up – V>0 – loose voltage • I goes down – V<0 – gain voltage Inductor: currentlagsvoltage Lecture XVIII

  10. Current and voltage in AC circuit • t=0, current flows to capacitor •  gain charge  gain voltage • Current changes sign •  drain charge  loose voltage Capacitor: voltagelagscurrent Lecture XVIII

  11. Energy in AC circuit Energy of the magnetic field stored in an inductor Lecture XVIII

  12. Energy in AC circuit Energy of the electric field can be stored in a capacitor Lecture XVIII

  13. LC circuit • Two forms of energy: • Electric – in a capacitor • Magnetic - in solenoid • Analogy with a mass on a spring, two forms of energy • Kinetic • Potential • Oscillator! • No energy is lost, it is just changing its form Lecture XVIII

  14. Energy in AC circuit Power dissipated: P=I2R=RI20cos2wt Energydissipated Lecture XVIII

  15. LCR circuit • Resistors dissipate energy • Convert electrical energy into thermal energy • Resistor acts like friction for a weight on a spring • Damped oscillator! Lecture XVIII

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