Ohm’s Law� Electric Current

� Electric Potential

� Resistance

� Ohm’s Law

� Power

� Electromotive Force (emf)

� Homework

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Electric Current� Electric current is defined as the net rate of flow of charge through a cross-section of a conductor

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– For constant current

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– The unit of current is the ampere (A)

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� From conservation of charge

– I is the same in any cross-section of the conductor

– analogous to water flow in a pipe

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Electric Potential� Consider a charge q moving from point A to point B in an electric field

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� The work done by

� � as q moves from A to B is

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� The change in potential energy is defined to be the negative of the work done by

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Electric Potential (cont’d)

The potential difference between points A and B is defined as the change in potential energy per unitcharge

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� The unit of electric potential is the volt (V)

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� We often set a reference point, called ground, to have an electric potential of zero volts and thendetermine the electric potential at all other points relative to this reference point

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Resistance and Ohm’s Law� The resistance of a conductor is defined as the ratio of the potential difference across the conductor

to the current flowing through it

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� The unit of resistance is the ohm (� )

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� For many materials, the resistance is constant over a wide range of applied voltages and thisbehavior is known as Ohm’s law

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Resistivity� For a conductor of length � and cross-sectional area� the resistance is

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where � is the resistivity of the material (units:� m)

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Power� The electric potential energy converted to heat by a charge � � moving through a potential differ-

ence � � is

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� If the material is ohmic (resistor)

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Electromagnetic Force (emf)� Any device that increases the potential energy of a circuit by maintaining a potential difference

between points in a circuit while charges move through the circuit is called a source of electro-motive force (emf)

� The emf is defined as the work done per unit charge by the device

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� An ideal emf device is one that lacks any internal resistance

� Any real emf device, such as a battery, has internal resistance

� The rate at which energy is delivered by the emf is� �

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� � ��� � " �

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emf (cont’d)� From conservation of energy, the rate at which electric energy is delivered by the emf is equal to

the rate at which electric energy is converted to heat in the resistances of the circuit shown below

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� The terminal voltage of the battery is

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Example

The circuit elements in the circuit below have the following values: " $ = 4.4 V, " = 2.1 V, r $ = 2.3� ,r = 1.8� , and R = 5.5� . (a) What is the current I in the circuit? (b) What is the potential differencebetween the terminals of battery 1?

r2

ε2

r1

ε1

Battery 1 Battery 2

R

I

I

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Homework Set 12 - Due Wed. Feb. 11� Read Sections 21.1 - 21.6

� Answer Questions 21.3, 21.5, & 21.10

� Do Problems 21.9, 21.15 & 21.23

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