Chapter 27a - Resistive Circuits Last time we considered the simplest possible circuit R V A resistor connected to each terminal of a power supply

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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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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 26-9). 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.
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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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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
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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 counter-clockwise 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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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.

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Chapter 27a - Resistive Circuits Last time we considered the simplest possible circuit R V A resistor connected to each terminal of a power supply

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