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Unit 2.2 - Resistors Dividers

# Unit 2.2 - Resistors Dividers - Resistors in Series and...

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9/20/10 Dr. Bruce McCann 1 1 Resistors in Series and Parallel 3 Resistors in Series I S + - V S R 2 R 1 + - V 1 + - V 2 R 3 + - V 3 +V 1 +V 2 +V 3 -V S = 0 V 1 = I S R 1 V 2 = I S R 2 V 3 = I S R 3 KVL: Ohm’s Law: Substitute and solve: V S = I S R 1 + I S R 2 + I s R 3 V S = I S (R 1 + R 2 + R 3 ) 4 Resistors in Series I S + - V S R 2 R 1 + - V 1 + - V 2 R 3 + - V 3 V S = I S (R 1 + R 2 + R 3 ) This equation looks like Ohm’s Law: V S = I S R eq where R eq = R 1 + R 2 + R 3 5 Equivalent Resistors: Series R 2 R 1 R 3 R eq = R 1 + R 2 + R 3 Only the terminal behavior is preserved. The behavior of the individual resistors is lost. 6 Series Equivalents R 2 R 1 R 3 Only the terminal behavior is preserved. The internal details of the original circuit are lost. V 4 + - V 1 + - V 2 V 3 The arrangement of the elements in the circuit diagram is not important. + - V L R eq = R 1 + R 2 + R 3 + - V eq + - V L V eq = V 1 – V 2 + V 3 – V 4

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9/20/10 Dr. Bruce McCann 2 7 Alternative Equivalents Only the terminal behavior is preserved. R eq = R 1 + R 2 + R 3 V eq = V 1 – V 2 + V 3 – V 4 + - + - V L V eq R eq + - + - V L V eq R eq - + - + V L V eq R eq - + - + V L V eq R eq 8 Current Sources in Parallel I 1 - + V P I 2 I 3 I 4 I L KCL: I 1 – I 2 - I 3 + I 4 = I L I L - + V P I eq Equivalent Source: I eq = I 1 –I 2 – I 3 + I 4 9 Resistors in Parallel I 1 - + V P I 2 I 3 I S KCL: I 1 + I 2 + I 3 = I S R 1 R 2 R 3 KVL and Ohm’s Law: I 1 R 1 = I 2 R 2 = I 3 R 3 = V P V P /R 1 + V P /R 2 + V P /R 3 = I S V P (1/R 1 + 1/R 2 + 1/R 3 ) = I S (1/R 1 + 1/R 2 + 1/R 3 ) = 1/R eq 10 Equivalent Resistors: Parallel R 1 R 2 R 3 Only the terminal behavior is preserved. The behavior of the individual resistors is lost. 11 Parallel Resistors We often will use the shorthand notation: R 1 R 2 R 3 where signifies “in parallel with.” Note: No special notation is needed for series resistors. Use a “+” sign. R 1 R 2 R 3 12 Parallel Resistors: Example For resistors in parallel, the equivalent resistance is always smaller than the smallest resistor. 18 Ω 36 Ω 6 Ω
9/20/10 Dr. Bruce McCann 3 13 Why is the resistance smaller? + - 12 V 6 Ω 2 A + - 12 V 18 Ω 0.67 A + - 12 V 36 Ω 0.33 A + - 12 V R eq 3 A R eq = 12V/3A = 4.00 Ω R eq = 4.00 Ω + - 12 V 6 Ω 18 Ω 36 Ω 14 Two Resistors in Parallel Many times you will find only two resistors connected in parallel. What are some reasons you might do this? Increased power dissipation. Get a resistance value that you don’t have on hand. R 2 R 1 15 Two Resistors in Parallel R 1 R 2 This result does NOT generalize to three or more resistors in parallel. 16 Parallel Resistor Example R 1 = 20 Ω , R 2 = 30 Ω What is R 1 R 2 ? R

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Unit 2.2 - Resistors Dividers - Resistors in Series and...

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