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Last time we considered the simplest possible circuit,
V
R
A resistor connected to each terminal of a power supply that provides
a potential difference V between its terminals.
This obeys Ohm’s law (
V = iR
), so the current through the resistor
(and the wires) is
V
i
R
=
Resistive Circuits
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View Full Document So here, if
R
0,
However, this implies that if
R
0,
then the current becomes infinite.
R0
V
i(R
0)
lim
R
→
=
==
∞
You might think that
R = 0
is an impossible idealization but in fact
superconductors (for which R = 0 !) do exist (see HRW 269).
Moreover, the power dissipated by a resistor, and being delivered by
the power supply can be written,
2
V
P
R
=
2
V
P(R
0)
Lim
R
→
→=
=
∞
The power that must be delivered by the power supply becomes
infinite!
Real
power supplies
can
not
supply
infinite
current or
infinite
power.
A battery, for example, generates the charge it delivers to its
terminals via chemical reactions. Those reactions have maximum
rates at which they occur, so even if the circuit resistance allowed
for more current, the battery can’t deliver the charge at a faster rate
than it is produced.
All power supplies have similar limitations.
To account for the
real behavior of power supplies
we model them as
ideal power
supplies (which could deliver any current asked for)
except that they have an internal resistance, in series
with one or the
other output terminal (it doesn’t matter which).
Hence our real power supply (model) looks internally like this,
r
x
power supply
a
b
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View Full Document V
ba
r
x
The electromotive force
or EMF,
, (Xi pronounced zie) is the
ideal potential difference (in volts) that the supply produces
internally
, the internal resistance is
r
and the potential difference
between the supply output terminals is
V
ba
.
x
We now use this power supply in our simplest circuit to explore its
behavior.
r
x
R
a
b
a
b
Only differences in potential have physical meaning so we are free to
define the zero of potential wherever we want.
r
x
R
a
b
We set the potential equal to zero at point
a
and now consider what
happens to the potential as we travel
counterclockwise
around the
circuit.
From point
a
to the
negative terminal
(left side) of the ideal supply
the wire is a metal, which is an eqipotential so we remain at
V = 0
.
V = 0
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View Full Document r
V=
x
R
a
b
Inside
the the ideal supply, in going from the negative to the positive
terminal the potential difference is
raised
from 0 V to the EMF of the
ideal supply so the positive terminal is at
V =
x
, and since the wire up
to the internal resistor is an equipotential, this is the potential up to the
left side of the internal resistor r.
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This note was uploaded on 03/12/2010 for the course PHY PHY taught by Professor Mueller during the Spring '09 term at University of Florida.
 Spring '09
 MUELLER

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