Chapter 20
Circuit Elements
(capacitor, resistor, and Ohm’s law)
Capacitance


A capacitor is a device used in a
variety of electric circuits
The capacitance, C, of a capacitor is
defined as the ratio of the magnitude
of the charge on either conductor
(plate) to the magnitude of the
potential difference between the
conductors (plates)
Capacitor
Any two conductors separated by an insulator: capacitor
A
d
Q =CV
[C] = C/V = Farad
C
C = eoA/d
eo = 8.85x10-12 F/m
Parallel-Plate Capacitor


The capacitance of a device depends
on the geometric arrangement of the
conductors
For a parallel-plate capacitor whose
plates are separated by air:
A
C  eo
d
eo = 8.85x10-12 F/m
Parallel connection
Series connection
C1
C2
C1
C2
C3
C3
1/Ceq = 1/C1+1/C2+1/C3
Ceq = C1 + C2 + C3
Ceq
Example
Three capacitors C1=1F, C2=2 F,
C3=6 F. Find capacitance of the
equivalent capacitor.
Ceq
Applications of Capacitors –
Camera Flash

The flash attachment on a camera
uses a capacitor
• A battery is used to charge the
capacitor
• The energy stored in the capacitor is
released when the button is pushed to
take a picture
• The charge is delivered very quickly,
illuminating the subject when more light
is needed
Applications of Capacitors -Computers

Computers use
capacitors in many
ways
• Some keyboards use
capacitors at the
bases of the keys
• When the key is
pressed, the capacitor
spacing decreases and
the capacitance
increases
• The key is recognized
by the change in
capacitance
H-ITT remotes
• You can buy the remotes
from most bookstores.
Buy only the H-ITT remotes, no Turning point
remotes.
• Register remotes (if you got an email with the
score then you are ok).
• Tune remotes
• Answer the questions in class
• Look for your registration number on the screen.
In subsequent classes your number will appear in the
same spot.
• You have 4 attempts.
• Check your email for quiz scores
QUICK QUIZ
A capacitor is designed so that one plate is
large and the other is small. If the plates are
connected to a battery, (a) the large plate has
a greater charge than the small plate, (b) the
large plate has less charge than the small
plate, or (c) the plates have charges equal in
magnitude but opposite in sign.
QUICK QUIZ ANSWER
(c). The battery moves negative charge
from one plate and puts it on the other.
The first plate is left with excess positive
charge whose magnitude equals that of
the negative charge moved to the other
plate.
Electric Current



Whenever electric charges of like
signs move, an electric current is
said to exist
The current is the rate at which
the charge flows through the wire
The SI unit of current is Ampere
(A)
q
• 1 A = 1 C/s
I
t
Electric Current, cont

The direction of current flow is the
direction positive charge would flow
• This is known as conventional current flow


In a common conductor, such as copper, the current
is due to the motion of the negatively charged
electrons
It is common to refer to a moving charge
as a mobile charge carrier
• A charge carrier can be positive or negative
Current: amount of charge flowing
through a point per unit time
Current flows from higher potential to lower potential
I
Ohm’s law
e
e
e=RI
R
I
e
Example
In a tv tube, 5 x 1014 electrons shoot
out in 4 s. What is the electric
current?
Resistance


In a conductor, the voltage applied
across the ends of the conductor is
proportional to the current through
the conductor
The constant of proportionality is the
resistance of the conductor
V
R
I
Resistance, cont

Units of resistance are ohms (Ω)
•1 Ω = 1 V / A

Resistance in a circuit arises due to
collisions between the electrons
carrying the current with the fixed
atoms inside the conductor
Ohm’s Law


Experiments show that for many
materials, including most metals, the
resistance remains constant over a wide
range of applied voltages or currents
This statement has become known as
Ohm’s Law
•V=IR

Ohm’s Law is an empirical relationship
that is valid only for certain materials
• Materials that obey Ohm’s Law are said to be
ohmic
V=RI
Resistance, R = V/I
[R] = V/A = W (Ohm)
For a fixed potential difference across a resistor,
the larger R, the smaller current passing through it.
Req
Parallel connection
Series connection
R1
R2
R1
R2
R3
R3
Req = R1 + R2 + R3
1/Req =
1/R1+1/R2+1/R3
Q2. What is the ratio of the current flowing
through each resistor (I1:I2) in the circuit?
R1 = 10
R2 = 30
6V
1.
2.
3.
4.
1:1
3:1
1:4
Need more info.
• Electrical wires can be bent and/or stret
• A Node point (branching point) can be m
along the wire.
There are n identical resistors connected in parallel.
Req?
1/Req = 1/R + 1/R + 1/R + … + 1/R
= n/R
Req = R/n
Ra
(1) 1/Req = 1/Ra + 1/Rb
(2) Req is smaller than Ra and Rb
Rb
20
25
Req ≈ 10
1000 = 1k
2
Req < 2
Practically all the current flows
Though the bottom one!!
Ohm’s law:
e = R·I
I = e/R
= (6 V)/(6 Ohm)
= 1.0 A
R1 = 6
6 V
What is the electric potential at ?
We cannot tell the absolute potential at this point.
If e at
is +6 V, then 0 V at
If e at
is +3 V, then -3 V at
For both, the potential diff. is 6 V.
To be able to specify absolute potential at a given point,
we need to specify a reference point “0” potential.
GROUND
R1 = 6
6 V
Then, e at
is +6 V.
e = “0”
e = 4 + 2 = 6 (V)
e = R2I = 4 (V)
e = R3I = 2 (V)
R1 = 6
R2=4
R3=2
6 V
e = 2 V