EE202_4_F2008

EE202_4_F2008 - Resistive Circuits Simplest element in...

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Resistive Circuits implest element in Circuits All conductors exhibit Simplest element in Circuits. All conductors exhibit properties that are characteristic of resistors Voltage is linearly proportional to current: V = RI hms Law This is called an element law (element is the resistor) Ohms Law EE202 Fall 2008 1
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Resistor Power resistor is a passive element since V=IR and V and I are A resistor is a passive element since VIR and V and I are defined using the passive convention: V I I 2 2 R RI VI P EE202 Fall 2008 2
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Circuits o far we have discussed voltages currents and resistors as So far we have discussed voltages, currents and resistors as single elements. In what follows, we consider the entire circuit – a collection of two terminal elements In this work we consider circuits consisting of two or more circuit elements connected by perfect conductors, i.e., R=0 in our wires ( lumped-parameter circuit ) ( p p node 2 EE202 Fall 2008 3 node 1 node 3
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Nodes odes represented by either dashed lines enclosing the node Nodes represented by either dashed lines enclosing the node, or by a dot representative of the entire node. This is clearer if we redraw the circuit: ode 2 node 2 node 1 node 2 node 3 node 1 node 3 EE202 Fall 2008 4
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Kirchhoff’s Current Law (KCL) he algebraic sum of the currents entering any node is zero 1. The algebraic sum of the currents entering any node is zero   0 i i i i 0 4 3 2 1 4 3 2 1 i i i i EE202 Fall 2008 5
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Kirchhoff’s Current Law (KCL) The algebraic sum of the currents leaving any node is zero 2. The algebraic sum of the currents leaving any node is zero       0 i i i i 0 4 3 2 1 4 3 2 1 i i i i EE202 Fall 2008 6
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Kirchhoff’s Current Law (KCL) The sum of currents entering any node equals the sum of 3. The sum of currents entering any node equals the sum of currents leaving the node : 3 4 2 1 i i i i EE202 Fall 2008 7
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Kirchhoff’s Current Law (KCL) eneral Statement: We can state this mathematically as: General Statement: We can state this mathematically as: 0 N n i where i n is the n th current entering (or leaving) the 1 n node and N is the number of node currents EE202 Fall 2008 8
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Does this always hold? hat if: What if: 0 N n i For example 1 n 123 ii i  r the charge entering the node is reduced by some amount 31 2 i  Or the charge entering the node is reduced by some amount ( ). That is, there is charge accumulating at the node. This violates our assumption of perfect conductors NOT CORRECT EE202 Fall 2008 9
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Examples Sum Entering = Sum Leaving   2 35 6 0 i  Sum Entering Node = 0 2 6 0 i 2 40 A i  EE202 Fall 2008 10 2 4A i
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Kirchhoff’s Voltage Law (KVL) he algebraic sum of the voltage ses round any closed path 1. The algebraic sum of the voltage rises around any closed path is zero 1 V 12 VV V V 3 3 0 V  V da = 0 3 00 V EE202 Fall 2008 11
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This note was uploaded on 10/31/2010 for the course EE 423 taught by Professor Mitin during the Spring '10 term at SUNY Buffalo.

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EE202_4_F2008 - Resistive Circuits Simplest element in...

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