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PHYS219 Fall semester 2014
Lecture 09: RC Circuits; Magnetism
Dimitrios Giannios
Purdue University
First Midterm (EXAM I)
• Date: Thursday, September 25 @ 8pm
• Place: Physics, Room 112
• Duration: 1 hour
• Material Chapters 17, 18, 19 from coursebook
• as covered in classroom
• Do NOT bring your own “cheat sheet” (relevant
equations will be provided)
• All cell phones/smart phones are to be deactivated
Circuits with capacitor
The capacitance C of a capacitor tells about its
ability to store charge
from experiment:
I
q∝ ΔV
q = C ΔV
q=CV
The RC Circuit – Charging the Capacitor
• Kirchhoff’s Rules can be applied to all kinds of circuits
• The change in the potential around the circuit is
• What is I?
• What’s new?: I (and q) will now be time dependent
Solving for q(t) and I(t)
constant number
Dq q e
+
- =0
Dt RC R
Solving this equation is a four-step process:
See Appendix
1. Solve:
2. A second solution is:
3.The most general solution will be:
4.Boundary Condition at t=0:
unknown constant
How to Realize the Boundary Conditions ?
Boundary Conditions:
at t=0, q(t=0)=0
How does q vary with time AFTER
switch is closed?
q
The
current
cannot last
forever.
Why?
???
???
t=0
t
Summary of Results
• The current in the circuit is
described by
• The voltage across the
capacitor is
• The charge is given by
• τ = RC and is called the time constant
Example
E=9V
R=10, 000 Ω
C=0.001 F
τ = RC=(R=10,000 Ω)(0.001 F)=10 s
Units: [Ω][F]=[V/A][C/V]=[C/A]=s
What is i) charge on the capacitor, ii) the voltage on the capacitor, iii) the
current in the circuit, and iv) the voltage across the resistor 2 s after
switch is closed?
Capacitor
Resistor
Magnetism
Name derived from rocks (lodestones,
naturally magnetized pieces of iron ore)
found in the province of Magnesia in
Greece
First reports – 2500 BC
Historically, more interesting than
electricity due to importance in early
navigation applications
Originally thought to be separate topic
from electrostatics/electricity
Today: Unified subject –
electromagnetism
Fundamental Property of Magnets
South ‘seeking’
pole
North ‘seeking’
pole
Magnetic
‘dipole’
Magnetic Poles Force between Magnets
Magnitude of
force depends on
pole strength
Action at a Distance
Gravity, electrostatic and magnetic forces are
non-contact forces. They act on objects that
are not touching each other.
A force field describes these actionat-a-distance forces.
Gravitational Field
Electric Field (E)
Magnetic Field (B)
Magnetic Field/Electric Field for Dipoles
Magnetic Field Lines B
Electric Field Lines E
Units: Tesla
Units: N/C or V/m
B is a
vector
1
1
B lines continuous
E is a vector
E lines begin/end on
sources/sinks
Key Point: No ‘magnetic’ charges!
Magnetic Field Strengths (typical values)
Situation
Magnetic Field
(Tesla)
Magnetic Field
(Gauss)
Interstellar space
~ 1 x 10-10 T
~ 1μ G
Earth’s Field
~ 0.5 x 10-4 T
~ 0.5 G
Bar Magnet (refrigerator)
~ 0.01 T
~ 100 G
Laboratory Electromagnet
~ 2 T
20,000 G
MRI unit (Hospital)
~ 0.5-3 T
5,000 – 30,000 G
Large Superconducting Magnet
~ 20 T
Pulsed Fields (non-destructive)
~ 100 T
Explosive Compression
(destructive)
~ 105 G
~ 1000 T
White Dwarfs
~10-104 T
Neutron Stars
~106-1011 T
up to 108 G
up to 1015 G!!!
10,000 Gauss = 1 Tesla
The earth acts like large magnet
Geographic N pole of
earth roughly
corresponds to
Geomagnetic S pole of
earth
Earth’s Magnetic Field
Earth’s Geomagnetic Pole wanders
over time
Magnetic Declination in
Indiana is about 3o W
Earth’s Magnetic Field & Northern lights
Most powerful Cosmic Magnets
Magnetized, Rotating
Neutron Stars (~1012 G)
Magnetars (~1015 G)
APPENDIX: The exponential function vs. time
At any time t, the
f(t) = e t
exponential function
has a slope that is
everywhere equal to
the function itself
Important Limits: