 # Chapter 17 Current and Resistance. Chapter 17 Objectives Describe electric current Relate current, charge, and time Drift speed Resistance and resistivity.

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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: I= Q ΔtΔt 1 A = 1 C 1 s

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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 R =  l 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 – T 0 )] R = R 0 [1 +  (T – T 0 )] Since R is directly proportional to 

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, T c, 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 = q  V –So the total power used during a transfer of electrical energy is: P =  Q  V /  t –And the amount of charge transferred in a unit of time is defined as the current. P = (  Q /  t )  V = I  V –By using Ohm’s Law to incorporate resistance we get P = I 2 R –If the voltage is unknown P = (  V) 2 / R –If the current is unknown

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