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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: I J n q vd A • 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: V I R 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 . 1V 1Ω 1A • The inverse of the conductivity of a material is its resistivity ; units ·m. 1 ρ σ • 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: ρl R A = o + o ··(T – To) 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 crosssectional 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 = Ro· + Ro··(T – To) • is the temperature coefficient of resistivity. • All electric appliances have a fixed resistance. • Electric circuits make use of resistors to control the current level in the circuit. Web Sites • Resistors and Resistor Color Code Calculator • Resistor Color Code • Ohm’s Law • Voltage Circuit Simulator