1.1 1.2 Circuit Basics Mark Redekopp VOLTAGE AND CURRENT 1.3 1.4 Current / Voltage Analogy Current and Voltage • Charge is measured in units of Coulombs - - - - - - • Current – Amount of charge flowing - through a _________ in a certain Charge = ___________ Conductive Material Water + v 2 - – Measured in _________ = Coulombs per second + + i Higher Lower Potential Potential U2 – Current is usually denoted by the variable, I + • Voltage – Electric ________ energy U + v 3 - – Analogous to mechanical potential energy - v 1 + U3 - - (i.e. _________ ) 1 - – Must measure ________________ points 5V Higher Voltage Source = – Measured in Volts (V) Potential - - Water Pressure – Common reference point: Ground (GND) = 0V - 3V • Often really connected to the ground Lower Potential GND
1.5 1.6 Meet The Components Kirchhoff's Laws • Common sense rules that govern current and voltage • Most electronic circuits are modeled – Kirchhoff's Current Law (KCL) i 1 i 2 with the following components – Kirchhoff's Voltage Law (KVL) • Kirchhoff's Current Law (KCL) • Resistor i 4 i 3 – The current flowing _____ a location An electronic – Property how well a material conducts (a.k.a. node) must equal the current component (e.g. resistor, transistor, etc.) flowing _____ of the location electrons – The sum of current at any location must • Capacitor & Inductor ___________ KCL says ___________ – Measures material's ability to store charge and energy • Transistor Transistor – Basic amplification or switching technology 1.7 1.8 Kirchhoff's Current Law Kirchhoff's Laws • Reminder: KCL says ________ = __________ - v 2 + • Kirchhoff's Voltage Law (KVL) - v 4 + i 2 i 1 U • Start by defining a __________ for each U2 – The sum of voltages around a 4 current - v 3 + - v 1 + - v 5 + ______ (i.e. walking around U U U – It does not matter what direction we choose KCL says __________…implies ______ 1 3 5 and returning to the – When we solve for one of the currents we may get a i 2 ______________ current i 1 ____________) must equal 0 – "Negative" sign simply means the direction is – Define "polarity" of voltage KVL says: ___________ of our original indication _______________ and then be consistent as you • In the examples to the right the top two KCL says ________…implies ________ _______________ go around the loop…obviously examples the directions chosen are fine i 2 i 1 _______________ when you solve you may find but physically in violation of KCL… a voltage to be negative which • …but KCL helps us arrive at a consistent + v 2 - KCL says ___________ means you need to result since solving for one of the current U2 values indicates… flip/reverse the polarity i 2 i 1 KVL says: + v 3 - – The ___________ of i1 and i2 are the same - v 1 + U U ___________ – They always flow in __________ direction of 1 3 ___________ each other (if one flows in the other flows out KCL says ___________ or vice versa)
1.9 1.10 Resistance and Ohm's Law Practice KCL and KVL • Measure of how hard it is Hint: Find a node or loop where there for current to flow through is only one unknown and that should • Use KCL to solve for i3, i4, and i6 the substance cause a domino effect • Resistance = NODE A + v 5 - U9 2A ________________ U5 + 9V - Large i4 Small – How much ______ do you Resistance Resistance + 6V - + 2V - U U have to put to get a certain • Use KVL to solve for v3, v8, v5 4 6 ______________ - 3V + 6A i6 NODE B • Measured in Ohms (___) U2 1A R • Ohms Law - v 3 + + 5V - - 1V + U U U – _________ or _________ 1 3 7 Schematic Symbol for – R __ => I ___ i3 a Resistor U8 NODE C + v 8 - 3A http://usc.scout.com/2/926916.html http://www.zimbio.com/photos/Marquise+Lee/Oregon+v+USC/9qQqBuy838Z 1.11 1.12 Series & Parallel Resistance Solving Voltage & Current • Series resistors = one Series Connections • Given the circuit to the right, let… � ������ after the next with no R1 R2 – Vs = +5V, R1 = 400 ohms, R2 = 600 ohms • Solve for the current through the circuit and �� other divergent path voltages across each resistors (i.e. V1 and V2) �� � ��� – Since everything is in _______, KCL teaches us � • Parallel resistors = R eff =______ that the current through each component must Spanning the same two be the ____, let's call it i • i = _______________________________ Parallel Connection points – This alone lets us compute V1 and V2 since ___________ says • Series and parallel R1 R2 • V1 = ______ and V2 = ______ • V1 = ___V and V2 = ___V resistors can be – Though unneeded, KVL teaches us that combined to an • ______________ or that Vs = V1 + V2 R eff = equivalent resistor with R eff value given as shown…
1.13 1.14 Voltage Supply Drawings Voltage Dividers Original Problem • • The voltage source in the left diagram (i.e. the – Vs = +5V, R1 = 400 ohms, R2 = 600 ohms circle connected to the "Rest of Circuit") is shown + V tot - • Recall our solution in an alternate representation in the right i �������� R1 R2 diagram (i.e. the triangle labeled "Vdd") ��� – i = Vs / (R1 + R2) = 5/1000 = 5 mA ������� In the left diagram we can easily see a KVL loop • – V1 = i*R1 = 2V and V2 = i*R2 = 3V +V1- +V2- available • When two resistors are in series we can deduce an • There is still a KVL loop available in the right Actual …will be drawn expression for the voltage across one of them diagram like this connection… – i = ____________________ If two resistors Rx and Ry – V1 = i*R1 and V2 = i*R2 are in series then voltage – Substituting our expression for i: across Rx is: � ������ �� � ������������������������������� � ___________________ �� This diagram is an �� � equivalent to the one ��� � • The voltage across one of the resistors is above. proportional to the value of that resistor and the total series resistance 1.15 1.16 Solving Voltage & Current Solving Voltage & Current • Reconsidering the circuit to the right with… • Consider the circuit on the right… � ������ ������ – Vs = +5V, R1 = 400 ohms, R2 = 600 ohms • What is the relationship between V1 and V3? �� • Solve for the current through the circuit and �� ������ voltages across each resistors (i.e. V1 and V2) �� Can you solve for the voltage V1 (in terms of � • ��� – We can use the voltage divider concept to � Vs, R1, R2, R3)? �� immediately arrive at the value of V2 �� � – V2 = �� � • Can you solve for the voltage V2 (in terms of Vs, R1, R2, R3)?
1.17 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
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