What is Lightning?
Lightning is an electric
discharge between the
base of a cloud and the
ground. An average
lightning strike delivers
about 1020 electrons and
carry a current of 10,000
Amps at 100 million
Volts.
Have you ever
wondered: (1) what
causes the bright flash
of light in a lightning,
and (2) how wide is
actually a lightning
strike?
What is Lightning?
Just before the lightning “strikes”, a
column of electrons if formed between
the bottom of the cloud to the ground.
The electrons come from the cloud and
ionized air molecules. Once the column
of electrons touches the ground,
electrons flow into the ground.
Collisions between electrons and air molecules within the column result in
a brilliant flash of light (due to radiative ion-electron recombination).
The linear charge density is λ~10-3 C/m. Assuming that air molecules
break down (ionize) in an electric field E ≥3×106 N/C, one can estimate the
radius of the electron column as r = λ / 2πε 0 E ≈ 6 m
The luminous portion of a lightning strike is smaller, perhaps ~ 0.5 m
Note: ground currents can also be lethal well outside the range of the
electron column
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28. Direct Current Circuits
28.1 Electromotive Force (emf)
28.2 Resistors in Series and in Parallel
Suggested HW problems Chp28: 6-11, 13-15
Simple Electric Circuit
Electromotive force (emf) of the source
= work per unit charge by the source
Va − Vb =
ε
Vc − Vd = IR
(Va − Vb ) − (Vc − Vd ) =
⇒
ε = IR
ε − IR = 0
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Mechanical Analog of an Electric Circuit
Real Source of efm
real battery = ideal battery + small resistor
ε − Ir = IR
ε
I=
U=
U ≡ Va − Vb
U
R+r
Terminal voltage U vs I for a
real battery (emf source)
3
Battery with internal resistance
Resistors in Series
Va − Vb
Va − Vc
Vb − Vc
!
Req =
Va − Vc
I
4
Resistors in Parallel
I = I1 + I 2
!
Req =
Va − Vb
I
Equivalent Resistance
• use the method of equivalent transformations
• use symmetry arguments when possible
5
Example: Equivalent Resistance
⇔
Req = ?
I , I1 , I 2 = ?
Example: Equivalent Resistance
Req ≡ Rab = ?
6
Example: Equivalent Resistance
Req ≡ Rab = ?
What can we do in this case ???
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