AC circuits Physics 114 362021 Lecture IX 1

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

Self inductance • Magnetic field in a solenoid • It creates a magnetic flux

Direction of induced emf • In accordance to Lenz law • I – increase

Current and voltage in AC circuit Drop of voltage over resistor (V) follows I

Current and voltage in AC circuit Drop of voltage = - emf 1. I

Current and voltage in AC circuit 1. t=0, current flows to capacitor gain charge

Energy in AC circuit Energy of the magnetic field stored in an inductor 3/6/2021

Energy in AC circuit Energy of the electric field can be stored in a

LC circuit • Two forms of energy: – Electric – in a capacitor –

LC circuit • Harmonic oscillations in the AC circuit. • No battery. Start with

Energy in AC circuit Power dissipated: P=I 2 R=RI 20 cos 2 wt Energy

LCR circuit • Resistors dissipate energy – Convert electrical energy into thermal energy •

Slides: 13

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AC circuits Physics 114 3/6/2021 Lecture IX 1

Math review • Integrals and derivatives of trig. functions: • Relations between trig functions: 3/6/2021 Lecture IX 2

Self inductance • Magnetic field in a solenoid • It creates a magnetic flux through itself In general by definition: • Self inductance of a solenoid 3/6/2021 Lecture IX 3

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 3/6/2021 Lecture IX 4

Current and voltage in AC circuit Drop of voltage over resistor (V) follows I Current and voltage in phase 3/6/2021 Lecture IX 5

Current and voltage in AC circuit Drop of voltage = - emf 1. I goes up – V>0 – loose voltage 2. I goes down – V<0 – gain voltage Inductor: current lags voltage 3/6/2021 Lecture IX 6

Current and voltage in AC circuit 1. t=0, current flows to capacitor gain charge gain voltage 2. Current changes sign 3. drain charge loose voltage Capacitor: voltage lags current 3/6/2021 Lecture IX 7

Energy in AC circuit Energy of the magnetic field stored in an inductor 3/6/2021 Lecture IX 8

Energy in AC circuit Energy of the electric field can be stored in a capacitor 3/6/2021 Lecture IX 9

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 3/6/2021 Lecture IX 10

LC circuit • Harmonic oscillations in the AC circuit. • No battery. Start with a charge on the capacitor. • Once the capacitor starts discharging, the current will flow through the inductor: • The net drop of voltage over closed circuit must be zero: 3/6/2021 Lecture IX 11

Energy in AC circuit Power dissipated: P=I 2 R=RI 20 cos 2 wt Energy dissipated 3/6/2021 Lecture IX 12

LCR circuit • Resistors dissipate energy – Convert electrical energy into thermal energy • Resistor acts like friction for a weight on a spring • Damped oscillator! 3/6/2021 Lecture IX 13