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

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

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

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

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

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

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

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.

All components connected in series have the same current flowing through them.
Is = Ir = Id = Ii = Ispk = Iu = If

All components connected in parallel have the same voltage across them

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

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

Circuit Analysis: Example 3

Summary Introduced Kirchoff’s Laws Resistor network simplification
Simple circuit analysis

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

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

Resistors Colour Codes

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

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%

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

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

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

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?