Physics 121: Electricity & Magnetism – Lecture 13

Carsten Denker

NJIT Physics DepartmentCenter for Solar–Terrestrial

Research

April 18, 2007 Center for Solar-Terrestrial Research

LC Oscillations

2

2E

qU

C 21

2BU Li1

LC

April 18, 2007 Center for Solar-Terrestrial Research

LC Oscillations (cont.)

Damped Oscillation

2

2

10

d qL qdt C

cosq Q t

sindq

i Q tdt

2

2

10

d q dqL R qdt dt C

/ 2 cosRt Lq Qe t

2 2

2cos2 2E

q QU t

C C

2 2

2sin2 2B

q QU t

C C

April 18, 2007 Center for Solar-Terrestrial Research

Alternating Current/Forced Oscillations

Whatever the natural angular frequency of a circuit may be, forced oscillations of charge, current, and potential difference in a circuit always occur at the driving frequency d.

AC: alternating current

DC: direct current

d: driving angular frequency

April 18, 2007 Center for Solar-Terrestrial Research

Resistive, Capacitive, & Inductive Load

Resistor Capacitor Inductor

R RV I R

C C CV I X

1C

d

XC

L dX L

L L LV I X

April 18, 2007 Center for Solar-Terrestrial Research

Series RLC Circuit

April 18, 2007 Center for Solar-Terrestrial Research

Series RLC Circuit (cont.)

Impedance

Current amplitude

Phase constant

Resonance

22L CZ R X X

22 1/

m m

d d

IZ R L C

tan L CX X

R

1d

LC

April 18, 2007 Center for Solar-Terrestrial Research

Power in Alternating–Current CircuitsRMS current

RMS voltage

RMS EMF

Average power

rms2

II

rms2

VV

rms2

2avg rmsP I R

avg rms rms cosP I

April 18, 2007 Center for Solar-Terrestrial Research

Transformers

Step–up transformer

Step–down transformer

Transformation of voltage

Transformation of currents

Load resistance

ss p

p

NV V

N

ps p

s

NI I

N

2

eqp

s

NR R

N