1.1 Unit 1 Circuit Basics KVL, KCL, Ohm's Law LED Outputs Buttons/Switch Inputs
1.2 VOLTAGE AND CURRENT
1.3 Current and Voltage - - - • Charge is measured in units of Coulombs - - - - • Current – Amount of charge flowing through a ___________in a certain Conductive Material _____________ (A Wire) – Measured in _________ = Coulombs per second Higher Lower Potential Potential – Current is usually denoted by the variable, I • Voltage – Electric _________ energy – Analogous to mechanical potential energy - - (i.e. ___________) - – Must measure ___________ points 5V Higher – Measured in Volts (V) Potential - - – Common reference point: Ground (GND) = 0V - 3V Lower • Often really connected to the ground Potential GND
1.4 Current / Voltage Analogy Charge = Water + v 2 - + + i U2 + U + v 3 - - v 1 + U3 1 Voltage Source = Water Pressure
1.5 Meet The Components • Most electronic circuits are modeled with the following components • Resistor R – Measures how well a material conducts C electrons • Capacitor & Inductor L – Measures material's ability to store charge and energy • Transistor Transistor – Basic amplification or switching technology
1.6 Kirchhoff's Laws • Common sense rules that govern current and voltage – Kirchhoff's Current Law (KCL) i 2 i 1 – Kirchhoff's Voltage Law (KVL) • Kirchhoff's Current Law (KCL) i 4 i 3 – The current flowing _____ a location An electronic (a.k.a. node) must equal the current component (e.g. resistor, transistor, etc.) flowing _____ of the location – …or put another way… – The sum of current at any location must KCL says _____________ _________
1.7 Kirchhoff's Current Law • Reminder: KCL says ____________________ i 2 i 1 • Start by defining a _________ for each current – It does not matter what direction we choose – KCL says _________…implies ______ When we solve for one of the currents we may get a _____________current i 2 i 1 – "Negative" sign simply means the direction is ___________ of our original indication • In the examples to the right the top two KCL says ________…implies ______ examples the directions chosen are fine i 2 i 1 but physically in violation of KCL… • …but KCL helps us arrive at a consistent result since solving for one of the current KCL says ______ values indicates… i 2 i 1 – The __________ of i1 and i2 are the same – They always flow in the ________ direction of each other (if one flows in the other flows out KCL says ______ or vice versa)
1.8 Kirchhoff's Voltage Law • Kirchhoff's Voltage Law (KVL) - v 2 + - v 4 + U2 U4 – The sum of voltages around a - v 3 + - v 1 + - v 5 + _____ (i.e. walking around and U U U 1 3 5 returning to the ___________) must equal 0 – Define "polarity" of voltage and KVL says: _______________ then be consistent as you go _______________ around the loop…obviously _______________ when you solve you may find a voltage to be negative which + v 2 - means you need to flip/reverse U2 the polarity KVL says: + v 3 - - v 1 + U U __________ 1 3 _______________
1.9 A Brief Summary • KCL and KVL are ___________ and ________ no matter what kind of devices are used – The yellow boxes could be ANY electronic device: resistors, batteries, switches, transistors, etc …KVL and KCL will still apply – In a few minutes, we'll learn a law that only applies to resistors (or any device that can be modeled as a resistor) • Some KVL or KCL equations may be KVL says: ____________ v 1 +v 2 +v 3 =0 – Writing the equation for loop {v1,v2,v3} and v 1 +v 2 +v 4 +v 5 =0 {v3,v4,v5} may be sufficient and writing -v 3 +v 4 +v 5 =0 {v1,v2,v4,v5} may not be necessary – But as a novice, feel free to _____________ • Kirchoff's Laws apply to non time-varying circuits or circuits in the steady-state
1.10 Nodes • (Def.) An electric node is U9 the junction of U5 ______________ devices U U connected by wires 4 6 • ________ voltage at any U2 point of the node U U U • How many nodes exist in 1 3 7 the diagram to the right? U8
1.11 Practice KCL and KVL Hint: Find a node or loop where there • is only one unknown and that should Use KCL to solve for i3, i4, and i6 cause a domino effect i9 NODE A + v 5 - U9 NODE D 1A U5 - 9V + i4 + 4V - + 3V - U U • Use KVL to solve for v3, v8, v5 4 6 - 5V + 1A i6 NODE B U2 1A - v 3 + + 5V - - 2V + U U U 1 3 7 i3 U8 NODE C 0.5A - v 8 + i8
1.12 Resistance and Ohms Law • Measure of how hard it is for current to flow through the substance • Resistance = __________________ Large Small – How much _________ do you Resistance Resistance have to put to get a certain U1 ___________ to flow • Measured in Ohms ( Ω ) R • Ohm's Law Schematic Symbol for – I = _____ or V = _____ a Resistor – R __ => I __ Ohm's Law ONLY applies to resistors (or devices that can be modeled as a resistor such as switches and transistors) http://usc.scout.com/2/926916.html http://www.zimbio.com/photos/Marquise+Lee/Oregon+v+USC/9qQqBuy838Z
1.13 Series & Parallel Resistance • Series resistors = same Series Connections R1 R2 current must pass through both • Parallel resistors = each R=R1+R2 R eff = _______ connects to the same two nodes (same voltage Parallel Connection different applied to both) R1 R2 • Series and parallel resistors can be combined to an equivalent resistor with R eff = value given as shown… For only 2 resistors, R eff this simplifies to:
1.14 Solving Voltage & Current • Given the circuit to the right, let… i + V1 - – Vdd = +5V, R1 = 400 ohms, R2 = 600 ohms • R1 Solve for the current through the circuit and + V2 - voltages across each resistors (i.e. V1 and V2) R2 + Vs – Since everything is in _______, KCL teaches us _ that the current through each component must be the _______, let's call it i • i = _________________________ – This alone lets us compute V1 and V2 since Ohm's law says + v 1 - • V1 = _____ and V2 = ______ i • V1 = ___ and V2 = ____ U1 – Though unneeded, KVL teaches us that - v dd + + v2 - U U • Vdd-V1-V2=0 or that Vdd = V1 + V2 3 2
1.15 Voltage Supply Drawings • The voltage source (Vdd) in the left diagram (i.e. the circle connected to the "Rest of Circuit") is shown in an alternate representation in the right Rest of diagram (i.e. the triangle labeled "Vdd") Vdd Circuit • In the left diagram we can easily see a KVL loop available • There is still a KVL loop available in the right …will be drawn Actual diagram connection… like this Tip : Vdd is the name of the source Vdd voltage used for digital '1' signals. GND i + V1 - i (0V) is often used for digital '0' signals. + V1 - R1 R1 + V2 - Both are drawings of R2 + the same circuit (i.e. Vdd _ + V2 - they are equivalent) R2
1.16 Shortcut: Voltage Dividers • A shortcut application of KVL, KCL, and Ohm's law + V tot - when two resistors are in series ( must be in series ) i R1 R2 • When two resistors are in series we can deduce an expression for the voltage across one of them +V1- +V2- – (1) i = ____ / _________; (2) V1 = i*R1; (3) V2 = i*R2 – Substituting our expression for i into (2) and (3) Voltage Divider Eqn: If two 𝑆1 𝑆2 resistors R1 and R2 are in 𝑊1 = 𝑊 𝑆1 + 𝑆2 𝑏𝑜𝑒 𝑊2 = 𝑊 𝑢𝑝𝑢 𝑢𝑝𝑢 𝑆1 + 𝑆2 series then voltage across • R1 is: The voltage across one of the resistors is proportional to the value of that resistor and the V1 = ________________ total series resistance – If you need 10 gallons of gas to drive 500 miles, how much gas you have you used up after driving 200 miles? • Gas = ______________, Mileage = _________________ Memorize this. We will use it often!
1.17 Solving Voltage & Current • Reconsidering the circuit to the right with… i + V1 - – Vdd = +5V, R1 = 400 ohms, R2 = 600 ohms • Solve for the current through the circuit and R1 + V2 - voltages across each resistors (i.e. V1 and V2) R2 + – We can use the voltage divider concept to Vs _ immediately arrive at the value of V2 – 𝑊2 =
1.18 Solving Voltage & Current • Consider the circuit on the right… + V3 - • What is the relationship between V1 and V3? R3 + V1 - • Can you solve for the voltage V1 (in terms of Vs, R1, R2, R3)? R1 R2 + Vs _ • Can you solve for the voltage V2 (in terms of Vs, R1, R2, R3)?
1.19 A Problem… • Given the following parameters… – Vs=5V, R1=4, R2 = 12, R3 = 2 and R4 = 10 ohms. • Can we use the voltage divider concept to immediately solve the voltage across R2 or do we need to first do some manipulation? What about R4? • First, find the total equivalent resistance (R eq ) seen by Vs and then solve for the voltage across each resistor First collapse this to a single equivalent resistance, R eq
1.20 …Continued (Blank Workspace)
1.21 LEDS AS OUTPUTS AND SWITCHES/BUTTONS AS INPUTS
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