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ECE201_Lecture05

ECE201_Lecture05 - 2 1 1 1 1 1 R R R R i i eq When there...

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1 ECE201 Linear Circuit Analysis I Lecture 5. Topics: R combinations, voltage & current division 1. Resistors in series add (1) equivalent resistance R eq , as seen by the source. Circuit elements to the right of AB need not be all resistors. R eq < 0 is OK. It can happen when dependent sources are present in the circuit. R eq is an abstract concept that satisfies v in = Req · i in (2) R eq for series resistance (3) General form Resistance in series add to form R eq . = i i eq R R + - Req B v in i in + v 1 R 1 A + v 2 + v 3 R 2 R 3 + - v in Req i in B A
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2 2. Voltage division v 1 v in = ? v 2 v in = ? v 3 v in = ? General Form: Voltage distributes around a series resister circuit in proportion to each branch R. ) ... , 3 , 2 , 1 ( n i R R v v i i i in i = = + - v in i in + v 1 + v 2 + v 3 R 1 R 2 R 3 +
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3 3. Conductances in parallel add (1) equivalent conductance G eq , as seen by the source G eq is an abstract concept that satisfies I in = G eq · v in Is G eq < 0 OK? (2) G eq for parallel resistance (3) General Form Conductances in parallel add to form Geq. = i i eq G G (4) Equivalently, + + = =
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Unformatted text preview: 2 1 1 1 1 1 R R R R i i eq When there are only resistors, then 2 1 2 1 2 1 1 1 1 R R R R R R R eq ⋅ + = + = and, 2 1 2 1 R R R R R eq + ⋅ == (5) Why R eq for series R, and G eq for parallel R? Simplicity!! ↑ i in A ↓ i 1 G 1 B Geq ↓ i 2 ↓ i 3 G 2 G 3 ⇔ ↑ A B + – + – i in v in Geq 4 4. Current Division i 1 i in = ? i 2 i in = ? i 3 i in = ? General Form Current distributes across a parallel resister circuit in proportion to each branch G. ) ... , 3 , 2 , 1 ( n i G G i i i i i in i = = ∑ ↑ i in ↓ i 1 G 1 ↓ i 2 ↓ i 3 G 2 G 3 + – v in 5 Practice Problem 1 . (1) Find R eq and G eq (2) Find V in 6 (3) Find V x (Hint: Use Voltage Division) (4) Find I y = I 6 Ω (Hint: Find I 3 first, then use Current Division) 7 Practice Problem 2 . Find R eq . Hint: Key is to find V in I in . 8 Practice Problem 3 : A Fun Example of Equivalent Resistance....
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