1. AC circuits
Physics 122
11/23/2018
Lecture XIX

2. Description of harmonic oscillator using complex numbers
w=2pf – cyclic frequency
I=I0sin(wt+d), d-phase at t=0, Calculations are greatly simplified by using complex numbers:
11/23/2018
Lecture XIX

3. Inductance Magnetic field in a solenoid
It creates a magnetic flux through itself
Changing magnetic flux generates emf = -drop of Voltage
11/23/2018
Lecture XIX

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
11/23/2018
Lecture XIX

5. AC circuits
External source of alternating voltage V(t)=V0sinwt – Forced oscillator
Frequency f, cyclic frequency w=2pf
Active elements
Inductors
Capacitors
Passive elements
Resistors
11/23/2018
Lecture XIX

6. Phasor diagram
Graphical way to present current and voltage in AC circuit
Present current and voltage in a certain element (resistor, inductance, capacitance) as vectors rotating in (x,y) plane
Vector length is equal to maximum possible value of I or V: I0 and V0
Vector projection on y-axis is equal to the value of current or voltage at the moment t x y I0
11/23/2018
Lecture XIX

7. Current and voltage in AC circuitx y I0 Vo
Drop of voltage over resistor (V) follows I
Current and voltage in phase
11/23/2018
Lecture XIX

8. Current and voltage in AC circuitx y I0 Vo
Inductor: current lags voltage
11/23/2018
Lecture XIX

9. Current and voltage in AC circuitx y I0 Vo
Capacitor: voltage lags current
11/23/2018
Lecture XIX

10. Energy in AC circuit
Energy of the magnetic field stored in an inductor
11/23/2018
Lecture XIX

11. Energy in AC circuit
Energy of the electric field can be stored in a capacitor
11/23/2018
Lecture XIX

12. LC circuit Two forms of energy: Oscillator!
Electric – in a capacitor
Magnetic - in solenoid
Oscillator!
When energy in the capacitance is at its maximum, energy in the inductance is at its minimum
No energy is lost, it is just changing its form
11/23/2018
Lecture XIX

13. LCR circuit x y I0 VR VL VC
Ohm’s law!!
11/23/2018
Lecture XIX

14. Impedance x I0 VR VL VC V0 y
This equation relates maximum voltage to maximum current.
Mind, that they do not happen at the same time. There is a phase shift between Imax and Vmax -f
11/23/2018
Lecture XIX

15. Phase angle and power factorx I0 VR VL VC V0 f
Cosf – power factor
NB. V and I are not real vectors, only in phasor diagram representation.
11/23/2018
Lecture XIX

16. Resonance in LCR circuit
Largest current when impedance is the smallest
XL, XC are functions of frequency
At a certain frequency
11/23/2018
Lecture XIX

17. Energy in AC circuit Total average power in AC
Power dissipated only in resistors:
11/23/2018
Lecture XIX