PHY 2049: Physics II

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402407 405767 416479 402614 406876 417029 432808 411209 420713 432798

Ch. 31 Electromagnetic Oscillations

RC, RL, LC circuits Driven damped Oscillations Resonance Series RLC circuits Power Transformer

Last time

LC circuit Analogous to a

pendulum L m q x C 1/k

Be careful with ωt in radians (not degrees)

C

q

C

qLiU

LCtqq

C

q

dt

qdL

o

ooo

22

1

2

1

1sin

0

222

2

2

Alternating Currents

A resistance

0

)sin(sin

0sin

tItR

VI

IRtV

R

o

The current and voltage are in phase

Capacitor: AC response

CX

tX

V

tItCVdt

dqti

tCVq

C

C

Co

o

1

)90sin(

)90sin(cos)(

sin

0

The current leads the voltage

Inductor: AC response

The current lags the voltage

LX

tX

Vt

L

Vti

tVdt

diLv

L

L

oo

oL

)90sin(cos)(

sin

HITT

A capacitor in an LC oscillator has a maximum potential difference of 15V and a maximum energy of 360 μJ. At a certain instant the energy in the capacitor is 40 μJ. At that instant what is the potential difference across the capacitor?

A. zero B. 5V C. 10V D. 15VE. 20V

An LC circuit has a capacitance of 30 μF and an inductance of 15mH. At time t = 0 the charge on the capacitor is 10 μC and the current is 20mA. The maximum charge on the capacitor is:

A. 8.9 μC B. 10 μC C. 12 μC D. 17 μC E. 24 μC

A different problem

Yet different A 45-mH inductor is connected to a source of

sinusoidal emf with a frequency of 400 Hz and a maximum emf of 20V. The maximum current is:

A. 0 B. 0.18A C. 1.1A D. 360A E. 2300A ans: B

RLC circuit

222'

'Rt/2L-

2

2

)2

(

)cos(Qe q

tcos

L

R

t

VC

q

dt

dqR

dt

qdL o

RLC circuit

R

XX

IZ

XXRIe

vvve

CL

CL

RCL

tan

22InductiveCapacitiveIn resonance

e = E sin ωt i = io sin (ωt –φ)Capacitor current leads

Power = I2R= ermsirmscosφ (cos φ =R/Z)

Resonance

Transformers