Prozorov_08 - PHYSICS 222 Introduction to Classical Physics...

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Unformatted text preview: PHYSICS 222 Introduction to Classical Physics II Prof. Ruslan Prozorov Iowa State University Fall 2011 LECTURE 8 Resistors in parallel & in series. Kirchhoff’s rules. Measuring instruments. electric circuits PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University 9 September 2011 2 resistors in circuits Rules and assumptions • Current is conserved (because charge is conserved!) • Wires are ideal (no resistance) unless otherwise indicated. So two points along the same wire have the same potential, or the voltage drop across a wire is zero. • A battery produces a fixed increase in potential PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University 9 September 2011 3 Resistors in series Two resistors R1 and R2 are in series when they are connected one after the other: A● R1 I The same current flows through both: I1 = I2 R2 B● PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University 9 September 2011 4 equivalent resistor The same current flows through the equivalent resistor: Ieq = I1 = I2 A● A● R1 I I R2 B● PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University Req B● 9 September 2011 5 same current, potentials add V1 = VA – VC V2 = VC – VB Veq V1 V2 IeqReq I1R1 I2R2 But I1 = I2 = Ieq, so Req R1 R2 Veq = VA – VB A● A● R1 Req C● R2 B● PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University B● 9 September 2011 6 many resistors in series R1 Req R1 R2 R3 ... R2 R3 … I eq I1 I2 I3 ... Veq V1 V2 V3 ... Note that Req Ri Use series connection to increase resistance PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University 9 September 2011 7 This is the mechanical equivalent of two resistors in series: R1 R2 R1 R2 = V1 + V2 I1 = I2 PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University 9 September 2011 8 current vs power The current thorough resistors in series is the same. The power dissipated in each resistor and the voltage across each resistor are NOT (unless they are identical resistors) Cu NiCr Cu NiCr Cu NiCr Cu NiCr I I Resistivities: RNiCr 50RCu NiCr 100 108 m Cu 2.0 10 8 m VNiCr 50 Cu V PNiCr 50PCu PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University NiCr glows! 9 September 2011 9 Resistors in parallel Two resistors R1 and R2 are in parallel when they are connected to the same potential difference VA - VB. A● I R1 R2 B● V1 = V2 (= VA – VB ) PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University 9 September 2011 10 same potential, currents divide Ieq I2 A● A● I1 R1 R2 B● Req B● I eq I1 I2 Veq V1 V2 Req R1 R2 V1 = V2 = Veq 1 Req 1 R1 PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University V I R 1 R2 9 September 2011 11 multiple resistors in parallel … 1 Req 1 R1 1 R2 1 R3 ... And remember that: Note that Req Ri … R3 R2 R1 Veq V1 V2 V3 ... I eq I1 I2 I3 ... Use parallel connection to decrease resistance PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University 9 September 2011 12 R1 In this case, R2 and R3 are in parallel to each other (and then in series with R1): R1 I1 Current splits I3 I2 V 2 = V3 R2 R3 R3 R2 I1 = I2 + I3 PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University 9 September 2011 13 two identical bulbs of resistance R 1 1 1 2 Req R R R draw two times more total current comparing to one bulb. However, current I through each bulb remains unchanged. 2 2 2 P Req R I tot I I 2 I ε I PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University Req I 9 September 2011 14 combinations of series and parallel PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University 9 September 2011 15 Kirchoff’s Rules - junctions o The algebraic sum of the currents into any junction is zero. PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University 9 September 2011 16 Kirchoff’s Rules II—loops o The algebraic sum of the potential differences in any loop, including those associated with emfs and those of resistive elements, must equal zero. PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University 9 September 2011 17 Kirchoff’s Rules - examples PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University 9 September 2011 18 Kirchoff’s Rules - examples PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University 9 September 2011 19 instruments: D’Arsonval’s galvanometer PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University 9 September 2011 20 The ammeter PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University 9 September 2011 21 Ammeters and voltmeters in combination PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University 9 September 2011 22 Ohmmeters and digital multimeters PHYS222 - Lecture 8 - Prof. Ruslan Prozorov - Iowa State University 9 September 2011 23 ...
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This note was uploaded on 11/14/2011 for the course PHYS 5863005 taught by Professor Meyer during the Fall '09 term at Iowa State.

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