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**Principles of Computer Engineering: Lecture 3: Kirchhoff’s Laws**

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**Kirchhoff’s Voltage Law (KVL)**

“The algebraic sum of all voltages around any closed path in a circuit is zero” (positive for a voltage rise, negative for a voltage drop. v1 v2 + – v3 Correct your lab manual p32

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**Kirchhoff’s Current Law (KCL)**

“The algebraic sum of all currents at any node (junction) in a circuit is zero” (positive for a current leaving a node, negative for coming a node) or restate as “ The sum of currents flowing into a junction is equal to the sum of currents flowing out a junction i1 i2 i3

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**Calculate the value of v, i and power dissipated in each resistor.**

vc is a rise in the direction of the current in the resistor. Vc = -1*20 = -20V P20Ω = i2R = 12*20 = 20 W Id in the 25Ω resistor is in the direction of the voltage rise across the resistor. id = -50/25=-2A P25Ω = v2/R = 502/25 = 100 W

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**Sum the current at each node**

Node a: i1 + i4 - i2 - i5 = 0 Node b: i2 + i3 – i1 - ib - ia= 0 Node c: ib – i3 – i4 - ic = 0 Node d: i5 + ia + ic = 0 Note: no connection dot ● in the centre of the diagram

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**Sum the voltage around each designated path in the circuit**

Path a -v1 + v2 + v4 – vb – v3 = 0 Path b -va + v3 + v5 = 0 Path c vb – v4 – vc – v6 – v5 = 0 Path d -va – v1 + v2 - vc + v7 – vd = 0

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Resistors Components which resist or reduce the flow of current in a circuit are called resistances, the unit of resistance is the ohm (Ω). They are used in circuits to control or limit the amount of current flow in a wire ,and to be a current-to voltage convertor. Resistors in series: R total =R1+R2+R3+R4 Resistors in parallel: 1/Rtotal = 1/R1 +1/R2 +1/R3 +1/R4 The total resistor of a parallel resistor network is always dominated by, and is less than, the smallest resistor.

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**All components connected in series have the same current flowing through them.**

Is = Ir = Id = Ii = Ispk = Iu = If

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**All components connected in parallel have the same voltage across them**

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**Circuit Analysis: Example 1**

Combining series and parallel resistors accordingly to simplify circuits and determine equivalent resistances 12 parallel with (10Ω+14Ω) Product over sum rule: 12*24/(12+24) = 8Ω 2, 6, and 8Ω connected in series 2+6+8 = 16Ω

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**Circuit Analysis: Example 2**

18 parallel with (3+6): 18*9/(18+9) = 6 is = 120/(4+6) = 12 A 120v = V4Ω +Vxy V4Ω = Is*R(4Ω) = 12*4 = 48 V Vxy = = 72 V i1 = Vxy/18 = 72/18 = 4 A i2 = Vxy/(3+6) = 72/9 = 8 A Confirm: is = i1 + i2

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**Circuit Analysis: Example 3**

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**Summary Introduced Kirchoff’s Laws Resistor network simplification**

Simple circuit analysis

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**Principles of Computer Engineering: Labs Experiment 3: Kirchoff’s Laws**

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Overview Build a simple resistor network and measure the voltages at each node Use results to verify Kirchoff’s Voltage Law Calculate the currents through each node and compare to Kirchoff’s Current Law

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**Resistors Colour Codes**

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Resistor Colour Codes Identify the following resistors based on their colour codes {1kΩ, 2.2kΩ, 3.9kΩ, 4.7kΩ & 5.6kΩ} Measure them and calculate actual error % Populate table with expected colour for each value Resistor Value Colour Band 1 Band 2 Band 3 Tolerance % Measured Value Error 1000Ω Brown Black Red 5 2200Ω 3900Ω Orange White 4700Ω Yellow Violet 5600Ω Green Blue

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**Test Resistor Network (KVL)**

Build the circuit below Use N0 as your reference node (0V) Test the voltages at each node using DVM Component V1 VR1 VR2 VR3 VR4 VR5 Voltage[V]±1%

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**Check each of three loops that KVL is preserved**

Loop 1 => – V1 + VR1 + VR2 = 0 or equivalently V1 = VR1 + VR2 Loop 2 => – VR2 + VR3 + VR4 = 0 or equivalently VR2 = VR3 + VR4 Loop 3 => – VR4 + VR5 = 0 or equivalently VR4 = VR5

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**Test Resistor Network (KCL)**

Calculate the currents passing in each loop from voltages measured previously. DO NOT MEASURE CURRENTS DIRECTLY Verify KCL at each node within error margins

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**Verify KCL at the two nodes (N2 and N3)**

Current # I1 I2 I3 I4 I5 Current [A] ±__% Node 2 => – I1 + I2 + I3 = 0 or equivalently I1 = I2 + I3 Node 3 => – I3 + I4 + I5 = 0 or equivalently I3 = I4 + I5

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**Summary Build resistor network and test Measure voltages at each node**

Calculate currents passing through each node Verify both KVL and KCL Consider sources of errors in this experiment Put all your results and notes into your logbook! Any questions?

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