26.27_Lec-12

26.27_Lec-12 - Physics 241 Lecture 12 Y. E. Kim September...

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Unformatted text preview: Physics 241 Lecture 12 Y. E. Kim September 30, 2010 Chapter 26, Section 3 Chapter 27, Sections 1 - 2 September 30, 2010 University Physics, Chapter 26 and 27 1 September 30, 2010 University Physics, Chapter 26 2 Chapter 26 Section 3 Multi-Loop Circuits ¡ To analyze a multi-loop circuit, identify all complete loops and all junction points in the circuit and DSSO\ .LUFKKRII·V Rules to these parts of the circuit separately ¡ Analyze the single loops in a multi-loop circuit with .LUFKKRII·V /RRS 5XOH DQG WKH MXQFWLRQV ZLWK .LUFKKRII·V Junction Rule, and obtain a system of coupled equations in several unknown variables ¡ These coupled equations can be solved in several ways ¡ Solution with matrices and determinants ¡ Direct substitution September 30, 2010 University Physics, Chapter 26 3 ([DPSOH¡ .LUFKKRII·V 5XOHV ¢£¤ ¡ The circuit here has three resistors, R 1 , R 2 , and R 3 and two sources of emf, V emf,1 and V emf,2 ¡ This circuit cannot be resolved into simple series or parallel structures ¡ To analyze this circuit, we need to assign currents flowing through the resistors ¡ We can choose the directions of these currents arbitrarily September 30, 2010 University Physics, Chapter 26 4 ¡ At junction b the incoming current must equal the outgoing current ¡ At junction a we again equate the incoming current and the outgoing current ¡ But this equation gives us the same information as the previous equation! ¡ We need more information to determine the three currents ² 2 more independent equations ([DPSOH¡ .LUFKKRII·V /DZV ¢£¤ 2 1 3 i i i ¡ 1 3 2 i i i ¡ September 30, 2010 University Physics, Chapter 26 5 ¡ 7R JHW WKH RWKHU HTXDWLRQV ZH PXVW DSSO\ .LUFKKRII·V Loop Rule. ¡ This circuit has three loops. ¡ Left ¡ R 1 , R 2 , V emf,1 ¡ Right ¡ R 2 , R 3 , V emf,2 ¡ Outer ¡ R 1 , R 3 , V emf,1 , V emf,2 ([DPSOH¡ .LUFKKRII·V /DZV ¢£¤ September 30, 2010 University Physics, Chapter 26 6 ([DPSOH¡ .LUFKKRII·V /DZV ¢£¤ ¡ Going around the left loop counterclockwise starting at point b we get ¡ Going around the right loop clockwise starting at point b we get ¡ Going around the outer loop clockwise starting at point b we get ¡ But this equation gives us no new information! 1 1 ,1 2 2 1 1 ,1 2 2 0 e m f e m f i R V i R i R V i R ¡ ¡ ¡ ¢ £ £ 3 3 ,2 2 2 3 3 ,2 2 2 0 e m f e m f i R V i R i R V i R ¡ ¡ ¡ ¢ £ £ 3 3 ,2 ,1 1 1 e m f e m f i R V V i R ¡ ¡ £ £ September 30, 2010 University Physics, Chapter 26 7 ¡ We now have three equations ¡ And we have three unknowns i 1 , i 2 , and i 3 ¡ We can solve these three equations in a variety of ways ([DPSOH¡ .LUFKKRII·V /DZV ¢£¤ 1 3 2 i i i ¡ 1 1 ,1 2 2 e m f i R V i R ¡ ¡ 3 3 ,2 2 2 e m f i R V i R ¡ ¡ 2 3 , 1 2 , 2 1 1 2 1 3 2 3 3 , 1 1 , 2 2 1 2 1 3 2...
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This note was uploaded on 09/09/2011 for the course PHYS 241 taught by Professor Wei during the Fall '08 term at Purdue.

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26.27_Lec-12 - Physics 241 Lecture 12 Y. E. Kim September...

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