Physics 1202: Lecture 7 Today’s Agenda Announcements: –Lectures posted on: –HW assignments, solutions etc. Homework #2:Homework #2: –On Masterphysics today: due Friday week –Go to masteringphysics.com Labs: Begin THIS week

Today’s Topic : Electric current (Chap.17) Review of –Electric current –Resistance New concepts –Temperature dependence –Electromotive force (battery) –Power –Circuits »Devices »Resistance in series & in parallel

 R I  = R I

Current Idea l Current is the flow of charged particles through a path, at circuit. l Along a simple path current is conserved, cannot create or destroy the charged particles l Closely analogous to fluid flow through a pipe.  Charged particles = particles of fluid  Circuit = pipes  Resistance = friction of fluid against pipe walls, with itself. E

Ohm's Law Vary applied voltage V. Measure current I Does ratio ( V / I ) remain constant?? V I slope = R = constant V I I R

Resistivity L A E j e.g, for a copper wire,  ~  -m, 1mm radius, 1 m long, then R .01  So, in fact, we can compute the resistance if we know a bit about the device, and YES, the property belongs only to the device !  

Make sense? L A E j Increase the Length, flow of electrons impeded Increase the cross sectional Area, flow facilitated The structure of this relation is identical to heat flow through materials … think of a window for an intuitive example How thick? How big? What’s it made of? or

Lecture 7, ACT 1 Two cylindrical resistors, R 1 and R 2, are made of identical material. R 2 has twice the length of R 1 but half the radius of R 1. –These resistors are then connected to a battery V as shown: V I1I1 I2I2 –What is the relation between I 1, the current flowing in R 1, and I 2, the current flowing in R 2 ? (a) I 1 < I 2 (b) I 1 = I 2 (c) I 1 > I 2

Lecture 7, ACT 2 R  I x Consider a circuit consisting of a single loop containing a battery and a resistor. Which of the graphs represents the current I around the loop?

Conductivity versus Temperature In lab you measure the resistance of a light bulb filament versus temperature. You find R  T. This is generally (but not always) true for metals around room temperature. For insulators R  1/T. At very low temperatures atom vibrations stop. Then what does R vs T look like?? This was a major area of research 100 years ago – and still is today. temperature coefficient of resistivity

Electromotive force Provides a constant potential difference between 2 points –  : “electromotive force” (emf)  R I I r V +-  May have an internal resistance –Not “ideal” (or perfect: small loss of V) –Parameterized with “internal resistance” r in series with  Potential change in a circuit  - Ir - IR = 0

Power Battery: Stores energy chemically. When attached to a circuit, the energy is transferred to the motion of electrons. This happens at a constant potential. »Battery delivers energy to a circuit. »Other elements, like resistors, dissipate energy. (light, heat, etc.) Total energy delivered not always useful. –How much energy does it take to light your house … well for how long? –Remember definition of Power (Phys. 1201).

Power Recall that In a circuit, where the potential remains constant. –Only q varies with time where

Power Batteries & Resistors Energy expended What’s happening? Assert: chemical to electrical to heat Charges per time Energy “drop” per charge Units okay? For Resistors: Rate is:

Power What does power mean? –Power delivered by a battery is the amount of work per time that can be done. i.e. drive an electric motor etc. –Power dissipated by a resistor, is amount of energy per time that goes into heat, light, etc. A light bulb is basically a resistor that heats up. The brightness (intensity) of the bulb is basically the power dissipated in the resistor. –A 200 W bulb is brighter than a 75 W bulb, all other things equal.

Batteries (non-ideal) Parameterized with “internal resistance” r in series with   : “electromotive force” (emf)  R I I r V Power delivered to the resistor R: P max when R/r =1 ! = V( I=0 )  - Ir - IR = 0  - Ir = V 

 R I  = R I

Devices Conductors: Purpose is to provide zero potential difference between 2 points. »Electric field is never exactly zero.. All conductors have some resistivity. »In ordinary circuits the conductors are chosen so that their resistance is negligible. Batteries (Voltage sources, seats of emf): Purpose is to provide a constant potential difference between 2 points. »Cannot calculate the potential difference from first principles.. electrical  chemical energy conversion. Non-ideal batteries will be dealt with in terms of an "internal resistance". +- V + - OR

Devices Resistors: Purpose is to limit current drawn in a circuit. »Resistance can be calculated from knowledge of the geometry of the resistor AND the “resistivity” of the material out of which it is made. »The effective resistance of series and parallel combinations of resistors will be calculated using the concepts of potential difference and current conservation (Kirchoff’s Laws). Resistance Resistance is defined to be the ratio of the applied voltage to the current passing through. V I I R UNIT: OHM = 

How resistance is calculated Resistance –property of an object –depends on resistivity of its material and its geometry Resistivity –property of all materials –measures how much current density j results from a given electric field E in that material –units are Ohm x m (  m) Conductivity –sometimes used instead of resistivity –measures the same thing as  Conductance –sometimes used instead of resistance –measures the same thing as R

Resistors in Series The Voltage “drops”: Whenever devices are in SERIES, the current is the same through both ! This reduces the circuit to: a c R effective a b c R1R1 R2R2 I Hence:

Another (intuitive) way... Consider two cylindrical resistors with lengths L 1 and L 2 V R1R1 R2R2 L2L2 L1L1 Put them together, end to end to make a longer one...

Resistors in Parallel What to do? But current through R 1 is not I ! Call it I 1. Similarly, R 2  I 2. How is I related to I 1 & I 2 ?? Current is conserved! a d a d I I I I R1R1 R2R2 I1I1 I2I2 R V V Very generally, devices in parallel have the same voltage drop  

Another (intuitive) way... Consider two cylindrical resistors with cross-sectional areas A 1 and A 2 Put them together, side by side … to make a “fatter” one with A=A 1 +A 2, V R1R1 R2R2 A1A1 A2A2 

V R1R1 R2R2 V R1R1 R2R2 Summary Resistors in series –the current is the same in both R 1 and R 2 –the voltage drops add Resistors in parallel –the voltage drop is the same in both R 1 and R 2 –the currents add