circuits

circuits - Kirchoffs Laws Direct: KCL, KVL, Ohms Law V = IR...

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Kirchoff’s Laws Direct: KCL, KVL, Ohm’s Law VI R V GI =⇒ = GR = 1 Ohm’s Law: I 11 2 36 =⋅ =⋅ 23 12 =⋅ (always get 1 equation/Resistor) KCL: A: - + B: 50 123 III +−= −−+= eq. are dependent (in general, get n -1 indep. for nodes) KVL: −+ − = VV 12 24 0 write 1 loop equation for each loop with a voltage not in the current set of equations. Eliminate either V 1 or I using Ohm’s Law eq: A: −+ + − = 5 1 2 0 112 VVV −− = + 1 3 1 6 1 12 1 2 11 5 24 V V KVL: 24 0 Cramer’s Rule: AX B [] ⋅= vv X Det A B A Det A i ii N = −+ 01 1 .. .. 5 24 V + - 6 3 V 1 V 2 + I 1 I 2 - + 12 I 3 A B
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We can always write in terms of only V , or I variables using ohm’s law: KCL: A : −+ + = III 123 0 KVL: M 1 : 12 2 4 0 12 II M 2 : −+ −= 4680 231 −− = 111 24 0 84 6 0 12 0 1 2 3 I I I Note: if VI R = RG = 1 V I G R + B 2 6 4 12 V V 1 V 3 8 1 I A M 1 M 2 V 2 + + + - - + I 3 I 2 I 1 Current Dependent Voltage Source: +
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Rules for nodes: 1) Convert all voltage to current sources 1) Determine a reference node and identify unknown relative voltages 2) Use KCL at each unknown node: at node A: GV GV GV I AA A AB B AN N A −− = .... B: - AB A BB B BN N B +− = .... N: - AN A BN B NN N N = .... where: G ii all conductances connected to node i G ji all conductances between node i and node j I i all current sources connected to node i Define N equations in N unknowns all other voltages and currents by Ohm’s Law from V and S . 2 22 2 1 11 R V 10 5V 1 1 R V R + - ⇔⇔ I 1 2 A 10 1 Ω= . eg: 4 2 5 4 10 20 + - 9 A 12 V Eq: 3 A 1 4 Ref 1 10 1 20 1 4 1 2 1 5 9 A A B C
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A: 025 5 25 05 025 3 9 .. . . . ++ () −− = VV V AB C ( A ) B: . V A + −= 05 01 02 02 0 ... . BC C: .25 V A −+ + + = 02 025 005 9 . .
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This note was uploaded on 12/29/2011 for the course ENGR 5a taught by Professor Brewer during the Fall '09 term at UCSB.

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circuits - Kirchoffs Laws Direct: KCL, KVL, Ohms Law V = IR...

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