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25.26_Lec-11

# 25.26_Lec-11 - Physics 241 Lecture 11 Y E Kim Chapter 25...

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Physics 241 Lecture 11 Y. E. Kim September 28, 2010 Chapter 25, Sections 6 ² 7 Chapter 26, Sections 1 - 2 September 28, 2010 University Physics, Chapter 25 and 26 1

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September 28, 2010 University Physics, Chapter 25 2 Resistances in Parallel (1) ± Instead of connecting resistors in series so that all the current must pass through both resistors, we can connect the resistors in parallel such that the current is divided between the two resistors ± This type of circuit is shown below
September 28, 2010 University Physics, Chapter 25 3 Resistance in Parallel (2) ± In this case, the voltage drop across each resistor is equal to the voltage provides by the source of emf ± 8VLQJ 2KP·V /DZ ZH FDQ ZULWH WKH FXUUHQW LQ HDFK UHVLVWRU ± The total current in the circuit must equal the sum of these currents ± Which we can rewrite as 1 1 e m f V i R 2 2 12 iii ± 1 2 11 §· ± ± ± ¨¸ ©¹

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September 28, 2010 University Physics, Chapter 25 4 Resistance in Parallel (3) ± :H FDQ WKHQ UHZULWH 2KP·V /DZ IRU WKH FRPSOHWH FLUFXLW DV ± .. where ± We can generalize this result for two parallel resistors to n parallel resistors 1 e m f q iV R 12 11 1 ± 1 n i ¦ =
September 28, 2010 University Physics, Chapter 25 5 Example: Network of Resistors (1) ± Consider the network of resistors shown below ± Calculate the current flowing in this circuit.

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September 28, 2010 University Physics, Chapter 25 6 Example: Network of Resistors (2) ± First look for pairs of resistors: R 3 and 4 are in series ± Now note that 34 and 1 are in parallel 34 3 4 ± 13 4 134 134 1 34 1 34 11 1 or RR ± ±
September 28, 2010 University Physics, Chapter 25 7 Example: Network of Resistors (3) ± And now R 2 , 5 , 6 , and 134 are in series ± ² 123456 2 5 6 134 1 34 123456 2 5 6 1 34 13 4 123456 2 5 6 134 123456 e m f RR V i ³³³ ³ ³ ³³

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September 28, 2010 University Physics, Chapter 25 8 Example 2: More Resistors (1) ± The figure shows a circuit containing one ideal 12-V battery (no internal resistance) and 4 resistors with R 1 =20 ȍ , 2 =20 ȍ , 3 =30 ȍ , and 4 =8 ȍ . (Important note: Inputs are given by 2 significant numbers Æ answers should be rounded off to 2 significant numbers !) Question: What is the current through the battery? Answer: Idea: Find the equivalent resistance DQG XVH 2KP·V /DZ± 2 and 3 are in parallel.
September 28, 2010 University Physics, Chapter 25 9 Example 2: More Resistors (2) What is the current through the battery? ± R 23 =12 : ± 1 , 23 and 4 are in series. i V R 1234 12 V 40 : 0.3 A

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September 28, 2010 University Physics, Chapter 25 10 Example 2: More Resistors (3) ± The circuit contains one ideal 12 V battery (no internal resistance) and 4 resistors with R 1 =20 ȍ , 2 =20 ȍ , 3 =30 ȍ , and 4 =8 ȍ Question: What is the current i 2 through 2 ?
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25.26_Lec-11 - Physics 241 Lecture 11 Y E Kim Chapter 25...

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