Lecture 08 Current Resistance February 23 2005 Happenings

Lecture 08 Current & Resistance February 23, 2005

Happenings o Yesterday (Monday) n o Today n o We begin to study electric current and the concept of resistance. Tomorrow (Friday) n n n o We completed the topic of capacitance Continue with electric current QUIZ on the material from this week. Web. Assign on C is due Monday n Web. Assign on Resistance and current is due

New Topic n Current and Resistance Commercial Resistors Color Coded

Conductors n In the past we decided that in a conductor n n n The Electric Field is ZERO because we postulated that no charges were to move. Static Situation Any electric field must be at the surface That field must be normal to the surface Let’s look at another situation.

Consider a conductor V 1 V 2 Electric Field Walla …. . a CIRCUIT n n The mobile electrons can “move” under the influence of an electric field. We then have a “current” (to be defined) flowing in the wire. But WAIT … how can we? ? ? Only if …

From the Past Q Flows and then stops. Vo + -

A Different Situation Vo circuit n n Charge will begin to flow through the short. Charge can flow back into the battery and discharge it. Wire can get warm, emit light or even burn our (fuse). The FLOW of charge is defined as a current.

Current is a good thing

Franklin’s Impact on Physics!!! ELECTRONS CURRENT n n Positive charge will leave the battery from the positive terminal and flow through an external circuit to the negative terminal. Electrons will go the other way. Current is defined as the flow of POSITIVE CHARGE. + charge does not normally flow in a wire.

Definition n Current is the total amount of charge that flows through a “wire” in one second. Current is measured in Coulombs per second. A current of one coulomb per second is defined as an AMPERE. (Amp. )

CONCISE DEFINITION: CURRENT Current will flow throughout the cross-section of the wire (usually). Current through aa’ is the same as the current through bb’ and cc’. What is DIFFERENT between aa’ and bb’ with respect to current?

What’s Different? ? i=5 amps A=. 1 m 2 CURRENT DENSITY A=0. 05 m 2 J=5 amps/. 05 m 2 = 100 amps/m 2 J=5 amps /. 1 m 2 = 50 amps/m 2

Current can’t “pile up” at a point n a circuit.

Example First introduction to Kirchoff’s Node Equation

Consider 3 A ^ 5 A 2 A v 6 A 8 A

Question: A 5 Amp current is set up in a circuit for 6 minutes by a 6 Volt Battery. How much chemical energy is provided by the battery? Vo + CIRCUIT OF SOME SORT - WORK (Energy) per unit Charge = q. V

Definition wire i V High Low Current increases with Potential Difference (V) Ohm’s Law

Observations n n n Wires and Resistors are made from conducting materials. These materials have some fundamental properties associated with them. Electrons are attached to atoms. n n Outer electrons weakly bound Small Force (Applied Electric Field) can easily push them. They bump into things which retard their motion. The more things that retard their motion, the more difficult it is to push a current via an applied potential difference. n Thus, the resistance goes up.

What kinds of things cause resistance? n n Sudden Constrictions in the conductor including bends! Underlying structuren n Amorphous Crystalline n n n Defects Impurities Thermal Collisions n Temperature

Fundamental Property RESISTANCE vs. RESISTIVITY n n n Consider a wire made of some material. Resistance is a property of the rire itself … the material and the shape. New Quantity: n RESISTIVITY is a property of the material itself regardless of its shape/

Consider our wire: L A V n What would happen to the current if we n n n Increased the voltage? Increased the Area? Increased the length?

Summary R is called the RESISTANCE and is measured in OHMS (W)

Define CONDUCTIVITY s

Resistivity – Ohm-Meters Silver Copper Aluminum Tungsten Platinum Silicon-Pure Glass Fused Quartz 1. 62 x 10 -8 1. 69 2. 65 5. 25 10. 6 2. 5 x 103 1010 to 1014 ~1016

WIRES American Wire Gauge Diameter - mm 30 gauge 0. 255 24 0. 511 18 (typical household) 1. 024 14 1. 628 12 2. 05

BACK TO OHM V=i. R i=V/R

Not EVERYTHING is a resistor The Semiconductor Diode

Effect of Temperature

Temperature Linear over a limited temperature range.

Question. For an 18 gauge wire of length L to have a resistance of 1 ohm what must L be if the material is copper? (d for 18 gauge is about 1 mm)

A current of 6. 5 Amps exists in a 9 Ohm resistor for 5 minutes. How many coulombs and how many electrons pass through the resistor in this time? Coulombs: 6. 5 COULOMBS per Second for 5 minutes 6. 5 C x 5 min X 60 sec/min = 1950 coulombs Number of electrons = # coulombs / electron charge = 1950 / 1. 6 x 10 -19 = 1. 22 x 10 +22

Microscopic Theory

J and E

Consider a wire

Micro-View “Resistivity” t depends on the material and is the mean time between collisions ease of motion – mobility resistance to motion - scattering

Power Battery supplies energy to the resistor which, in turn, dissipates it in the form of heat. + V i E L E C T R O N s Work done on charge Q = Q x V - REMEMBER: P=i. V and P=i 2 R

The Spectrum of Conductors ENGINEERED MATERIALS!!! Semiconductors

When 105 volts are applied across a wire that is 12 meters long and has a 0. 30 mm radius, the current density us 1. 7 x 10 4 A/m 2. What is the resistivity of the wire? ? From the current density we can find the CURRENT. i=JA = 1. 7 x 104 amp/m 2 X (p X 0. 32) mm 2 X (1 m/1000 mm)2 I = 4. 8 ma R= V/i = 105 volts / (4. 8 x 10 -3) amps = 2. 18 x 104 ohms r = 2. 18 x 104 ohms x 3 x 10 -7 m 2 / 12 m = 0. 005 ohm-meters

The figure below gives the electrical potential V(x) along a copper wire carrying a uniform current, from a point at higher potential (x=0 m) to a point at a lower potential (x=3 m). The wire has a radius of 2. 45 mm. What is the current in the wire? What does the graph tell us? ? *The length of the wire is 3 meters. *The potential difference across the wire is 12 m volts. *The wire is uniform. Let’s get rid of the mm radius and convert it to area in square meters: A=pr 2 = 3. 14159 x 2. 452 x 10 -6 m 2 or A=1. 9 x 10 -5 m 2 copper 12 volts 0 volts Material is Copper so resistivity is (from table) = 1. 69 x 10 -8 ohm meters