Ohm’s Law and Resistance AP Physics C Montwood High School R. Casao

Current Density J For a conductor of cross-sectional area A carrying current I, the current density J is: The current density is in the direction of motion of the charges for positive charge carriers and opposite the direction of motion for negative charge carriers.

Ohm’s Law A current density J and an electric field E are established in a conductor when a potential difference is maintained across the conductor. – – If the potential difference is constant, the current in the conductor will also be constant. Ohm’s law: J =  ·E  = conductivity

Ohm’s Law Ohm’s law states that for many materials (including most metals), the ration of the current density and electric field is a constant , which is independent of the electric field producing the current. The most common form of Ohm’s law is:

Resistance The motion of a ball rolling down an inclined plane and bouncing off pegs in its path is analogous to the motion of an electron in a metallic conductor with an electric field present.

Resistance If some of the pegs were removed, the ball would experience less resistance to its movement. If more pegs were added the ball might experience more resistance to its downhill motion. At the atomic level, currents are pictured as the flow of the outer electrons of atoms through the material. Resistance results from collisions of electrons with other electrons and with atoms. Resistance is the opposition to the flow of charge in a conductor.

Resistance Resistance is measured in ohms . The inverse of the conductivity  of a material is its resistivity  ; units  ·m. Resistivity is related to the nature of the material. Good conductors have low resistivity (or high conductivity). Poor conductors have high resistivity (or low conductivity). Resistance: Resistivity:  =  o +  o ·  ·(T – T o )

Resistance The resistance of a conductor is proportional to the length. – – Resistance increases with increased length. The resistance of a conductor is inversely proportional to the cross-sectional area of the conductor. – – Resistance decreases with increased cross- sectional area. Resistance is also dependent upon the temperature of the conductor. Collisions of electrons with other electrons and with atoms raises the temperature of a material as the added heat energy causes the electrons to move faster and hence collide more often. This increases the resistance of the conductor.

Factors Affecting Resistance

Resistance and Temperature R = R o · + R o ·  ·(T – T o ) R = R o · + R o ·  ·(T – T o )  is the temperature coefficient of resistivity.  is the temperature coefficient of resistivity. All electric appliances have a fixed resistance. All electric appliances have a fixed resistance. Electric circuits make use of resistors to control the current level in the circuit. Electric circuits make use of resistors to control the current level in the circuit.

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