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Chapter 17 Current and Resistance Chapter 17 Objectives • • • • • • • Describe electric current Relate current, charge, and time Drift speed Resistance and resistivity Behavior of resistors Superconductors Electric power Current • Electric current, I, is the rate at which electric charges move through a given area. – It would be like standing in front of Burger King and count all the cars traveling down Henry Street over a given time period. • For our purposes, we will consider the traveling of positive charges from positive fields to negative fields. I + - Drift Speed • The electric force due to an electric field present causes electrons to flow. • The electrons do not flow in a straight line, but rather in a zigzag path. • The nature of the path is due to the collisions of the electrons with other atoms in the conductor. • The electrons flow opposite of the direction of the force due to the nature of electric charges repelling like charges. – Remember that a negative electron flowing to the negative post of the battery would actually repel. • So some work is required to move that electron. • And that work can only be done by the electric potential energy that was stored in the voltage source. • Since the pattern is unpredictable, we can only come up with an average speed. • The net speed of a charge carrier moving in an electric field is known as drift speed. Amperes • The SI unit for measuring current is an ampere, A. • Remember current is the rate of flow of electric charges, so the formula looks like: Q I= Δt 1A=1C 1s Resistance • The resistance of a conductor is the ratio of voltage across the conductor to the current flowing through the conductor. – Resistance can be thought of as a conducting material that alters the flow of charge carriers through the circuit. – Resistors can be • light bulbs • appliances • a new material • SI unit is called an ohm. – Denoted • R – Symbol • Ω • Symbol in a circuit is: Ohm’s Law • Georg Simon Ohm (1787-1854) found that for many materials, including most metals, the resistance of the material is constant over a wide range of voltages. – That is Ohm’s Law in theory • During his experiments, he noticed that the relationship between current and voltage were proportional to one another in an ohmic material. – An ohmic material is one in which the resistance remains constant. • Since the resistance is constant, the relationship between voltage and current is written in the more useful form of Ohm’s Law: V = I R Resistivity • With Ohm’s discovery that the resistance is constant for a material under any voltage, that brings about the question: – Is the resistance the same for every material? • The answer is that the every material has its own, unique ability to resist charge flow. • That ability to resist charge flow is the resistivity, , characteristic of the material. • The resistivity of a material is: – proportional to its length, l. • longer distance means more time for charge to flow – inversely proportional to its area, A. • two lane highway versus a four lane highway l R= A Temperature v Resistance • In general, the resistivity of a material increases as temperature increases. – This is due to the atoms inside the material becoming more excited from the increased kinetic energy. – The extra excitement causes them to vibrate faster, which creates more collisions with the charge carriers as they attempt to pass through. • Each material has a different rate at which temperature can excite its atoms. • Remember the specific heat capacity concept! – Thus we must account for this difference in the form of the temperature coefficient of resistivity, . = 0[1 + (T – T0)] Since R is directly proportional to R = R0[1 + (T – T0)] Superconductors • There are some metals and other compounds whose resistances fall to virtually zero when they are cooled. • When cooled such that their temperature falls below the critical temperature, Tc, the resistance of the material becomes next to nothing. • These materials are called superconductors. – They include metals such as Al, Sn, Pb, Zn, Hg, In, Nb. • Copper, silver, and gold are great conductors but do not exhibit the properties of a superconductor. • An interesting phenomenon of superconductors is that once a current is established in them, the current will persist without any applied voltage. – This has lead to extensive research to find a superconductor with a critical temperature in a moderate range to allow for technology to exist in our lives that can power themselves! Semiconductors • Another altering phenomenon of electrical current can increase the resistance of a material as the voltage increased. – This increase in both resistance and voltage leads to an nonlinear increase in the current flow in a circuit. • These nonohmic materials are called semiconductors. – Often called diodes. • They act much like a gate or a valve for the current. – Semiconductors will allow current flow in certain directions, and greatly restrict the flow in other directions. • Diodes are often used in circuitry for electronic devices to send specific coded signals, and also to prevent back flow of current that could overload the device. • Semiconductors behave like resistors, so use the same sign conventions. – However, Ohm’s Law does not directly apply to semiconductors. • The symbol in a circuit is: Grounded Circuit • Quite often a circuit is grounded to ensure a complete transfer of charge from the positive terminal. – Most house circuits are grounded as a safety precaution so that any excess charge goes to the ground and not back into the circuit where it does not belong and may do damage. • For calculation purposes, a grounded location allows us to identify a place where PE = 0 J. • The symbol in a circuit for a ground is: + - Electrical Power • Recall the definition of power is the rate at which work is performed. • P = W/t – Thanks to the Work-Kinetic Energy Theorem: • W = KE – And Conservation of Energy states: • KE = PE – And the electrical potential energy can be found by: • PE = qV – So the total power used during a transfer of electrical energy is: • P = QV/t – And the amount of charge transferred in a unit of time is defined as the current. • P = (Q/t)V = IV – By using Ohm’s Law to incorporate resistance we get • P = I2R – If the voltage is unknown • P = (V)2 / R – If the current is unknown