### PRELAB 3: ELECTRIC CIRCUITRY

```PRELAB 3: ELECTRIC CIRCUITRY
A. ELECTRIC CURRENT AND CIRCUIT
Electric charge Q is a fundamental property of matter. Charges are measured in
Coulombs [C], which is a large number. An electron carries a unit of negative charge −e,
a proton carries a unit of positive charge +e, and neutrons carry no charge. Each unit of
charge is e=1.602×10–19C. An atom is made of electrons orbiting outside a nucleus,
which is composed of protons and neutrons, called nucleons. The oxygen-16 nucleus is
composed of 8 protons, and 8 neutrons. Thus the charge of an oxygen nucleus is +8e. The
radius of nucleus is of the order of 10–14 to 10–15 m, depending on the number of
nucleons. Atoms are normally neutral, and thus the number of electrons is equal to the
number of protons. The neutral atom of oxygen-16 is made of an oxygen nucleus and 8
electrons orbiting outside the nucleus.
Matters can be classified into conductors and insulators. Some materials are called semiconductors. A conductor has “free” electrons that can move in the presence of electric
potential, an applied voltage, resembling a ball falling from a height by the gravitational
potential. When electrons move in a conductor, we call electric current flows in the
conductor. The electric current is I=∆Q/∆t, the flow rate of charge flow per unit time.
Since the charge of electrons is negative, the current is flowing opposite to the direction
of electrons.
As electric potential is applied to an electric circuit, electric current flows from the high
voltage point to a lower voltage point, resembling water flows from higher ground to
lower position. The electric potential is measured in Volts, and the electric current is
measured in Amperes, related by the Ohm’s law: V=IR. Here V is the electric potential
in Volts, I is the electric current in Amperes, and R is the resistance (impedance)
measured in Ohms (Ω).
Major electric circuit elements are resistors, capacitors, and inductors. Resistors are
made of materials impede motion of electrons, capacitors are made of parallel plates that
can hold charges, and inductors are made of coils that can hold magnetic energy. For
example, a car battery is typically 12 V. Connect the battery to a 1000Ω resistor, the
current in the circuit is I=12V/1000Ω=12 mA=0.012 A.
a. The home electric outlet is typically 120 V. When connected to a light bulb that
has filament with 240 Ω resistor, what is the current flowing through the light
bulb?
I=
A.
b. Charge of an electron is
c. Charge of a carbon nucleus (made of 6 protons and 6 neutrons) is
1
A capacitor (also known
n as condensser) is norm
mally made o f two conduucting plates.. If
ppositive charrges Q are pllaced on onee plate, negattive charges –Q will be induced on tthe
oother plate. An
A electric potential
p
V an
nd electric field
fi will be eestablished bbetween thesse
ttwo plates. Thus
T
a capaccitor can sto
ore electric energy!
e
Thee positive chharge plate hhas a
hhigher potential. The cap
pacitance C is
i given by C=Q/V.
C
The capacitancee is measuredd in
F
nce of capaciitors is measuured in picoofarad or pF, i.e.
nF]=1000[pF
F].
A
An inductorr is made of conducting coils.
c
As thee electric currrent flows, m
magnetic fieeld is
induced. Wh
hen conductin
ng wires aree closely wou
und around a cylinder, eelectric field is
eenhanced at the
t inner tub
be of the cyliinder, and caanceled eachh other outsiide the cylindder.
T
Thus the ind
ductor can store
s
magneetic energy. The voltagee between tw
wo ends of ann
inductor is eq
qual to ∆V=L
L(∆I/∆t), wh
here L is the inductance. The amountt of energy sstored
in an inducto
or is equal to
o (½)LI2, wheere I is the current
c
in Am
mpere, and L is the
m
in Henry
H
[H], and
a energy stored
s
in the inductor is m
measured in
inductance measured
JJoules [J]. Ty
ypical inductance of indu
uctors are measured
m
in m
milli-henry [[mH]=10–3 H and
H
Henry [H].
B
B. PRO
OPERTIE
ES OF A RESONA
ANCE:
O
Often a systeem has naturral frequenciies of vibratiion. In a collumn of air in the PVC tuube,
tthe natural frrequencies are called thee harmonic frequencies,
fr
f 1, f2,…. A vibrating soource,
ssuch as the speaker, can drive the column of air. As the freqquency, f, off the driver
((speaker) is slowly
s
varied, the amplittude of the driven
d
system
m (air colum
mn) gets largeer
aand larger un
ntil it reaches a peak at one
o of its ow
wn resonant ffrequencies, f1, f2,…. W
When
w
we sweep thee speaker freequency pastt one of the harmonic
h
freequencies off the air coluumn,
w
we hear the increase
i
in amplitude
a
off the vibrating air columnn as an increease in loudnness
oof the radiateed sound from the tube. At resonancce the drivinng system paasses energy very
eefficiently on
n to the driveen system an
nd the ampliitude of the ddriven system
m reaches a
m
maximum caalled Amax. (See
(
Rossing
g, the Sciencce of Sound, Ch. 4.) A grraph of the
aamplitude ass a function of
o frequency
y is shown beelow.
2
The reson
nant amplitud
de peaks at frequency
f
f0 and that thee peak has a width, ∆f caalled the
line-width
h. The line-w
width is usuaally measure d at amplituude of 71% oof Vmax. For a system
which losses energy raapidly throug
gh damping or friction, tthe maximum
m amplitudee, Vmax, is
small and
d the line-wid
dth large, an
nd the resonaance is said tto be broad. Similarly, ffor a
resonating
g system wh
hich loses energy very sloowly, the maaximum ampplitude is veery large
and the lin
ne-width is very
v
small. The resonannce is said too be sharp.
The quality, Q, characcterizes the sharpness
s
off one of the rresonances. For examplle, for
the fundam
mental frequ
uency the Q value is:
f
Q 0.
(1.0)
f
A high Q system is on
ne with a shaarp resonancce. Once sett oscillating it loses enerrgy very
k is an exam
mple of an obj
bject with a vvery high Q. To drive ann object
slowly. A tuning fork
with high Q, the driviing frequenccy must be veery close to the resonantt frequency, f0.
C. ELECTRIC
L
C RESONA
ANCE OF
F LC CIR
RCUIT
A system of electric circuit
c
can allso have a reesonance. Sinnce capacitoors can store electric
energy an
nd inductors can store maagnetic enerrgy, a circuitt made of a ccapacitor, a rresistor,
and an ind
ductor in serries can beco
ome
a resonant circuit. Ressembling sim
mple
harmonic oscillators that
t can
transform
m gravitationaal potential
energy to kinetic enerrgy and vice
versa, LC
C circuit can transform
electric en
nergy to mag
gnetic energy
y
and vice versa.
v
Such a circuit form
ms a
resonancee circuit. Ressistors are
dissipativ
ve, resemblin
ng friction. The
T
RLC electric circuit iss shown belo
ow.
1
nance frequeency of this circuit
c
is f 0 
The reson
2 LC
Here the capacitor
c
C is
F], the inducctance L is inn Henry [H]], and the ressulting
resonancee frequency f0 is in Hertzz or [Hz] or [[1/s]. Typicaal number off L is in mH
H (10–3H)
to H, and C is 100 pF to 10000 pF
F, where 1 p
pF = 1×10–122 F. As the frrequency of the sine
wave generator is varried at constaant input volltage Vin, thhe output volltage Vout shhows a
maximum
m at the reson
nance frequeency f0, whicch is analog to the resonaance frequenncy of a
simple haarmonic oscillator. Find the
t resonancce frequencyy of the folloowing RLC ccircuits
with
a) L=
= 100 mH, C=1000
C
pF,
b) L=
= 1 H, C=1000 pF,
f0=
f0=
3
D
Data shown below
b
is a ty
ypical experiimental dataa for an RLC
C circuit. Plot Voltage vss
ffrequency an
nd find the resonance
r
freequency f0 and
a find the Q
Q-value. (Yoou can make a bbetter
bby using the wh
hole scale of ho
orizontal axis from
f
200 to 80
00 Hz, and the vvertical scale ffrom 0.5 V to 33.5 V.)
Frequency
y (Hz)
200
250
300
350
400
450
500
550
600
650
700
750
800
Output volltage (V)
1.19
1.32
1.52
1.82
2.27
2.83
3.00
2.43
1.78
1.33
1.03
0.834
0.692
T
The resonancce frequency
y of the abov
ve data is f0=
T
The Q value is Q=
4
```