Circuit Theory Laws - Lancaster High School

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Digital Electronics TM1.2 Introduction to AnalogCircuit Theory LawsCircuit Theory LawsThis presentation will Define voltage, current, and resistance. Define and apply Ohm’s Law. Introduce series circuits.o Current in a series circuito Resistance in a series circuito Voltage in a series circuitCircuit Theory Laws Define and apply Kirchhoff’s Voltage Law. Introduce parallel circuits.Digital Electronicso Current in a parallel circuito Resistance in a parallel circuito Voltage in a parallel circuit Define and apply Kirchhoff’s Current Law.Electricity – The Basics2Voltage, Current, & ResistanceCurrent – Current is the flow of electricalcharge through an electronic circuit. Thedirection of a current is opposite to thedirection of electron flow. Current ismeasured in AMPERES (AMPS).An understanding of the basics of electricityrequires the understanding of three fundamentalconcepts. Voltage Current ResistanceA direct mathematical relationship exists betweenvoltage, resistance, and current in all electroniccircuits.Project Lead The Way, Inc.Copyright 20093Andre Ampere1775-1836French Physicist41

Digital Electronics TM1.2 Introduction to AnalogCircuit Theory LawsVoltageResistanceVoltage – Voltage is the electrical force thatcauses current to flow in a circuit. It ismeasured in VOLTS.Resistance – Resistance is a measure ofopposition to current flow. It is measured inOhms.Alessandro Volta1745-1827Italian PhysicistGeorg Simon Ohm1789-1854German Physicist5First, An Analogy6Anatomy of a FlashlightThe flow of water from one tank to another is a good analogy foran electrical circuit and the mathematical relationship betweenvoltage, resistance, and current.Force: The difference in the water levels VoltageFlow: The flow of the water between the tanks CurrentOpposition: The valve that limits the amount of water atteryBlock Diagram7- BatterySchematic Diagram8OppositionProject Lead The Way, Inc.Copyright 20092

Digital Electronics TM1.2 Introduction to AnalogCircuit Theory LawsFlashlight SchematicCurrent Flow Conventional Current assumesthat current flows out of thepositive side of the battery,through the circuit, and back tothe negative side of the battery.This was the conventionestablished when electricity wasfirst discovered, but it is incorrect!CurrentResistance- Voltage- Closed circuit (switch closed) Open circuit (switch open) Current flow No current flow Lamp is on Lamp is off Lamp is resistance, usesenergy to produce light (andheat) Lamp is resistance, but is notusing any energy Electron Flow is what actuallyhappens. The electrons flow outof the negative side of the battery,through the circuit, and back tothe positive side of the battery.10Ohm’s Law The direction that the current flows does not affect what thecurrent is doing; thus, it doesn’t make any difference whichconvention is used as long as you are consistent. Both Conventional Current and Electron Flow are used. Ingeneral, the science disciplines use Electron Flow, whereasthe engineering disciplines use Conventional Current. Since this is an engineering course, we will use ConventionalCurrent.ConventionalCurrent11Project Lead The Way, Inc.Copyright 2009ElectronFlow9Engineering vs. ScienceElectronFlowConventionalCurrent Defines the relationship between voltage, current, andresistance in an electric circuit Ohm’s Law:Current in a resistor varies in direct proportion to the voltageapplied to it and is inversely proportional to the resistor’s value. Stated mathematically:I VR IV-RWhere: I is the current (amperes)V is the potential difference (volts)R is the resistance (ohms)3

Digital Electronics TM1.2 Introduction to AnalogCircuit Theory LawsOhm’s Law TriangleExample: Ohm’s LawExample:VII RVIR RV(ohms, )IV I R ( volts, V )VIThe flashlight shown uses a 6 volt battery and has a bulbwith a resistance of 150 . When the flashlight is on, howmuch current will be drawn from the battery?V(amperes, A )RR14Example: Ohm’s LawCircuit ConfigurationComponents in a circuit can be connected in oneof two ways.Example:The flashlight shown uses a 6 volt battery and has a bulbwith a resistance of 150 . When the flashlight is on, howmuch current will be drawn from the battery?Solution:Schematic DiagramIRParallel Circuits Components are connectedend-to-end. There is only a single path forcurrent to flow. Both ends of the components areconnected together. There are multiple paths for currentto flow.V VT Series CircuitsVRIR-IR VR6V 0.04 A 40 mAR 150 15Components16(i.e., resistors, batteries, capacitors, etc.)Project Lead The Way, Inc.Copyright 20094

Digital Electronics TM1.2 Introduction to AnalogCircuit Theory LawsSeries CircuitsExample: Series CircuitCharacteristics of a series circuit The current flowing through every series component is equal. The total resistance (RT) is equal to the sum of all of the resistances(i.e., R1 R2 R3). The sum of all of the voltage drops (VR1 VR2 VR2) is equal to thetotal applied voltage (VT). This is called Kirchhoff’s Voltage Law.VR1IT -Example:For the series circuit shown, use the laws of circuit theory to calculatethe following: The total resistance (RT) The current flowing through each component (IT, IR1, IR2, and IR3) The voltage across each component (VT, VR1, VR2, and VR3) Use the results to verify Kirchhoff’s Voltage Law.IT --- -IR3RTExample: Series CircuitVR2IR217VR3-VT-RTVR1IR1 VR2VT -18 VR3Example: Series CircuitSolution:Total Resistance:Solution:Voltage Across Each Component:R T R1 R2 R3VR1 IR1 R1 R T 220 470 1.2 k (Ohm' s Law)VR1 6.349 mA 220 Ω 1.397 voltsR T 1890 1.89 k VR2 IR2 R2 (Ohm' s Law)Current Through Each Component:VR2 6.349 mA 470 Ω 2.984 voltsIT VTRT(Ohm' s Law)12 vIT 6.349 mAmp1.89 k VIVR3 IR3 R3 (Ohm' s Law)RVIRVR3 6.349 mA 1.2 K Ω 7.619 voltsSince this is a seriescircuit :IT IR1 IR2 IR3 6.349 mAmp19Project Lead The Way, Inc.Copyright 2009205

Digital Electronics TM1.2 Introduction to AnalogCircuit Theory LawsExample: Series CircuitParallel CircuitsCharacteristics of a Parallel CircuitSolution:Verify Kirchhoff’s Voltage Law: The voltage across every parallel component is equal. The total resistance (RT) is equal to the reciprocal of the sum of thereciprocal: 1 1 111VT VR1 VR2 VR312 v 1.397 v 2.984 v 7.619 vRT12 v 12 v R1 R2 R3RT 111 R1 R 2 R 3 The sum of all of the currents in each branch (IR1 IR2 IR3) is equalto the total current (IT). This is called Kirchhoff’s Current Law.IT VR1VT-- VR2 VR3--2122RTExample: Parallel CircuitExample: Parallel CircuitExample:For the parallel circuit shown, use the laws of circuit theory to calculatethe following: The total resistance (RT) The voltage across each component (VT, VR1, VR2, and VR3) The current flowing through each component (IT, IR1, IR2, and IR3) Use the results to verify Kirchhoff’s Current Law.ITIR1IR2 VR1VT--1111 470 2.2 k 3.3 k R T 346.59 RT IR3 VR2Solution:Total Resistance:1RT 111 R1 R 2 R 3 Voltage Across Each Component:VR3-Since this is a parallelcircuit :VT VR1 VR2 VR3 15 volts-232324RTProject Lead The Way, Inc.Copyright 20096

Digital Electronics TM1.2 Introduction to AnalogCircuit Theory LawsExample: Parallel CircuitExample: Parallel CircuitSolution:Current Through Each Component:Solution:Verify Kirchhoff’s Current Law:VR1(Ohm' s Law)R1VR115 vIR1 31.915 mAmpsR1 470 IT IR1 IR2 IR3IR1 IR2 VR215 v 6.818 mAmpsR2 2.2 k IR3 VR315 v 4.545 mAmpR3 3.3 k IT 43.278 mAmps 31.915 mA 6.818 mA 4.545 mA43.278 mAmps 43.278 mAmpsVIRVT15 v 43.278 mAmpRT346.59 2526Summary of Kirchhoff’s LawsKirchhoff’s Voltage Law (KVL):The sum of all of the voltage drops in aseries circuit equals the total appliedvoltage.Gustav Kirchhoff1824-1887German PhysicistKirchhoff’s Current Law (KCL):The total current in a parallel circuit equalsthe sum of the individual branch currents.27Project Lead The Way, Inc.Copyright 20097

Circuit Theory Laws o Circuit Theory Laws 2 This presentation will Define voltage, current, and resistance. Define and apply Ohm’s Law. Introduce series circuits. o Current in a series circuit Resistance in a series circuit o Voltage in a series circuit Define and appl

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