cjurban,
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If the battery is zero for our potential, the battery imbues the circuit with some potential difference which creates a current.
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If a battery puts out zero volts, then it is dead and no current exists.
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My book says that the resistor will suck all of the potential energy out of the charges passing through it, since the voltage drop through the resistor equals the voltage of the battery.
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Of course. If you make a battery supply a current continuously, eventually it will deenergize.
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I don't understand how this could be, because if the charges in the wire have no potential energy after they've passed through the resistor how could they continue to be drawn toward the other end of the battery?
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Voltage is the electrical density of the charge (joules/coulomb). If the energy density at one point is more (higher voltage) than the energy density (lower voltage) at another point, then the charge will flow to the lower energy density provided there is a conduction path.
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Also, what happens as charge flows through a wire attached to both terminals of a battery, with no other circuit components, if we assume the resistance to be "negligible?" According to V=IR, the voltage would go to zero!
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You would have an infinity of current across a infinitesimal amount of resistance. That cannot happen in the "real" world. It is like asking the question of what happens when a unstoppable force encounters an immovable wall. It is more a philosophical question than a scientific one.
Ratch