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Physics 1402: Lecture 10 Today’s Agenda Announcements: –Lectures posted on: www.phys.uconn.edu/~rcote/ www.phys.uconn.edu/~rcote/ –HW assignments, solutions etc. Homework #3:Homework #3: –On Masterphysics : due Friday at 8:00 AM –Go to masteringphysics.com

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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

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

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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

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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

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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 =

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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

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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:

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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...

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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

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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

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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

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Lecture 10, ACT 1 I have two identical light bulbs. First I hook them up in series. Then I hook them up in parallel. In which case are the bulbs brighter? (The resistors represent light bulbs whose brightness is proportional to P = I 2 R through the resistor.) V R R A) SeriesB) ParallelC) The same R R

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I1I1 R R R I2I2 I3I3

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Kirchoff's First Rule "Loop Rule" or “Kirchoff’s Voltage Law (KVL)” "When any closed circuit loop is traversed, the algebraic sum of the changes in potential must equal zero." This is just a restatement of what you already know: that the potential difference is independent of path! We will follow the convention that voltage gains enter with a + sign and voltage drops enter with a - sign in this equation. RULES OF THE ROAD: R1R1 R2R2 I Move clockwise around circuit: R1R1 R2R2 I IR 1 IR 2 0 0 KVL:

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Loop Example a d b e c f R1R1 I R2R2 R3R3 R4R4 I KVL:

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Lecture 10, ACT 2 Consider the circuit shown. –The switch is initially open and the current flowing through the bottom resistor is I 0. –After the switch is closed, the current flowing through the bottom resistor is I 1. –What is the relation between I 0 and I 1 ? (a) I 1 < I 0 (b) I 1 = I 0 (c) I 1 > I 0 R 12 V R I

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Kirchoff's Second Rule "Junction Rule" or “Kirchoff’s Current Law (KCL)” In deriving the formula for the equivalent resistance of 2 resistors in parallel, we applied Kirchoff's Second Rule (the junction rule). "At any junction point in a circuit where the current can divide (also called a node), the sum of the currents into the node must equal the sum of the currents out of the node." This is just a statement of the conservation of charge at any given node.

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