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The Electronvolt When an electron (charge e) travels through a potential difference of 1 V (ie, when it moves from a given location to a location where the electric potential is 1 V higher), the electron loses e (1 V) 1602 10

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of electric energy and gains [Eq (1112)] the same amount of kinetic energy This quantity of energy is referred to as one electronvolt (1 eV) In general, any energy expressed in joules may be converted to electronvolts by dividing by 1602 10 19 J / eV The rate of ow of electric charge across a given conductor area is de ned as the electric current I through that area, or

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7 Electric Current, Resistance, and Power

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Also, in terms of J, the electric current through a surface S (eg, a cross section of the conductor) is I

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where dA dS cos is the projection of dS perpendicular to the ow direction, and J is the electric current density at a point within a conductor

CHAPTER ELEVEN

Ohm s Law Empirically, it is found that the current I in a resistor (long wire, conducting bar, etc) is very nearly proportional to the difference v in electric potential between the ends of the resistor This proportionality is known as Ohm s law:

(1117)

where the proportionality factor R is called the resistance The unit of resistance, 1 V / A The resistance of a conductor of length the ohm ( ), is de ned as 1 L and uniform cross-sectional area A is R L A (1118)

where , the resistivity, is a property of the material and is temperature-dependent m) The units of are ( The difference in potential between the terminals of any source of electric energy such as a battery or a mechanically driven generator, when delivering no current, is a measure of the electromotive force ve of the source Note that ve is often called the open-circuit voltage of a battery or generator The actual source of electric energy is

vt ve

(1119)

where vt is terminal voltage, I is the current passing through the source, and R0 is the internal resistance of the source The negative sign is used when the source is delivering current, and the positive sign is used when I has the opposite direction (eg, charging a storage cell) If an amount of charge dq moves through a difference in potential v, the change in electric energy is dE (dq)v (1120)

The electric power P is the time rate of change of electric energy, that is, P dE dt dq v dt I v (1121)

Note that (1 A)(1 V) 1 W or 1 V 1 W / A The power output of an energy source having terminal voltage vt and supplying current I is given as P I vt I(ve I R0) (1122)

The power absorbed by a pure resistance R when the potential difference across it is v1 2 is given by P I

v1 2

I 2R

v2 1 2

(1123)

This latter power is dissipated as heat

TOPICS IN APPLIED PHYSICS

8 Kirchhoff s Laws For any network composed of resistors and sources (batteries), given the values of a certain number of the electromotive forces ve, currents I, and resistances R, the values of the remaining quantities can be found by an application of Kirchhoff s laws

Kirchhoff s Junction Law The algebraic sum of all currents into any junction is zero That is, at any junction, I 0 (1124)

In the last equation, a current out of the junction is counted as negative Kirchhoff s Loop Law The algebraic sum of all electromotive forces around any closed circuit (loop) is equal to the algebraic sum of the voltage drops (the R IR and the R0 I) around the loop, that is,