1. AC circuits
Physics 114
11/27/2018
Lecture IX

2. Math review Integrals and derivatives of trig. functions:
Relations between trig functions:
11/27/2018
Lecture IX

3. Self inductance Magnetic field in a solenoid
It creates a magnetic flux through itself
Self inductance of a solenoid
In general by definition:
11/27/2018
Lecture IX

4. 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
11/27/2018
Lecture IX

5. Current and voltage in AC circuit
Drop of voltage over resistor (V) follows I
Current and voltage in phase
11/27/2018
Lecture IX

6. Current and voltage in AC circuit
Drop of voltage = - emf
I goes up – V>0 – loose voltage
I goes down – V<0 – gain voltage
Inductor: current lags voltage
11/27/2018
Lecture IX

7. Current and voltage in AC circuit
t=0, current flows to capacitor
 gain charge  gain voltage
Current changes sign
 drain charge  loose voltage
Capacitor: voltage lags current
11/27/2018
Lecture IX

8. Energy in AC circuit
Energy of the magnetic field stored in an inductor
11/27/2018
Lecture IX

9. Energy in AC circuit
Energy of the electric field can be stored in a capacitor
11/27/2018
Lecture IX

10. 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
11/27/2018
Lecture IX

11. 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:
11/27/2018
Lecture IX

12. Energy in AC circuit Power dissipated: P=I2R=RI20cos2wt
Energy dissipated
11/27/2018
Lecture IX

13. LCR circuit Resistors dissipate energy
Convert electrical energy into thermal energy
Resistor acts like friction for a weight on a spring
Damped oscillator!
11/27/2018
Lecture IX