ENGR-43_Lec-02-1_Ohms_Law.ppt 1 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engineering 43 Chp Ohm’s Law -

ENGR-43_Lec-02-1_Ohms_Law.ppt 2 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Chp.2 Outline  Introduce Basic Concepts And Laws That Are Fundamental To Circuit Analysis  Learning Goals Ohm’s Law - Defines The Simplest Passive Element: The Resistor Kirchhoff’s Laws - The Fundamental Circuit Conservation Laws –Kirchhoff’s Current (KCL) –Kirchhoff’s Voltage (KVL) Gustav Robert Kirchhoff:

ENGR-43_Lec-02-1_Ohms_Law.ppt 3 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Chp.2 OutLine cont. Learn To Analyze The Simplest Circuits –Single Loop → The Voltage Divider –Single Node-Pair → The Current Divider WYE ↔ Delta Transformation –A Technique To Reduce Common Resistor Connections That Are Neither Series Nor Parallel Circuits With Dependent Sources

ENGR-43_Lec-02-1_Ohms_Law.ppt 4 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Resistor  A Passive Element Characterized by an Algebraic Relation Between The VOLTAGE ACROSS its Terminals and The CURRENT THRU It The General Math/Physics Model  A Linear Resistor Obeys Ohm’s Law

ENGR-43_Lec-02-1_Ohms_Law.ppt 5 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Resistors cont.  Since The Equation Is Algebraic The Time Dependence Can Be Omitted  The Proportionality Constant, R, is called The RESISTANCE of the Element In Honor of German Physicist G. S. Ohm, The Units of R Are called Ohms, and Given the Symbol Capital Omega, Ω –From the Above Eqn, Discern the Ω Units

ENGR-43_Lec-02-1_Ohms_Law.ppt 6 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Resistors cont.  Most Common Multiples of Resistance kΩ = 10 3 Ω MΩ = 10 6 Ω  Most Common Practical Occurrence  Other V, I, R Combinations

ENGR-43_Lec-02-1_Ohms_Law.ppt 7 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Conductance = 1/Resistance  Recast Ohm’s Law to Find CURRENT as a Function of VOLTAGE:  G is Defined As CONDUCTANCE Has Units of Amp/Volt Called Siemens

ENGR-43_Lec-02-1_Ohms_Law.ppt 8 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Physical Realization Circuit Symbol

ENGR-43_Lec-02-1_Ohms_Law.ppt 9 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Linear Approximation  Real Resistors Are Generally Faithful to the Constant-R Approximation if Operated Within Specified V & I Ranges Linear approximation Actual v-I relationship Linear range

ENGR-43_Lec-02-1_Ohms_Law.ppt 10 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Special Cases - Shorts & Opens  Passive Convention ALWAYS Applies to R  Circuit Symbol Note Passive Sign Convention R = 0 G =  R =  G = 0  Special Cases

ENGR-43_Lec-02-1_Ohms_Law.ppt 11 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Ohm’s Law Problem Solving  Recall Ohm’s Law: I = 2[A] R = 5[Ω] V = IR + V = 20[V] - I = 4[A] R = V/I Given Any 2 Values, Can Find the 3 rd –Given Current & Resistance → Find Voltage –Given Current & Voltage → Find Resistance

ENGR-43_Lec-02-1_Ohms_Law.ppt 12 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Problem Solving cont. –Given Voltage and Resistance → Find Current I = V/R R = 4[Ω] + V = 12[V] -  Note The Use of the Passive Sign Convention In a Resistor, Current ALWAYS Flows V hi →V lo –Use VOLTAGE POLARITY Reference

ENGR-43_Lec-02-1_Ohms_Law.ppt 13 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  Conductance  Find i(t) Using Conductance Ohm’s Law using G

ENGR-43_Lec-02-1_Ohms_Law.ppt 14 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  Passive Sign Conv.  Find i(t) A B + V AB - I AB  When In Doubt, A-B it Voltage DROPS A→B Current FLOWS A→B  Using Ohm’s Law

ENGR-43_Lec-02-1_Ohms_Law.ppt 15 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Resistors and Electric Power  Resistors Are Passive Components That Can Only Dissipate Power Combining Ohm’s Law And The Expressions For Power We Can Derive Several Useful Relations –Four Variables (P,v,i,R) And Two Equations  Given Any Two Variables One Can Find The Other Two.

ENGR-43_Lec-02-1_Ohms_Law.ppt 16 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Solving Power Relations  Given: P, i  Given: v, R  Given: i, R  Given: P, R  Given: P, v

ENGR-43_Lec-02-1_Ohms_Law.ppt 17 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Power & Passive-Convention  If Not Specified, The Ref. Direction For V ExOR I Can Be Chosen, Then the Other Qty Given By The Passive Sign Convention  Units: Beware the Multiples V, A, W, Ω are SI units; mA, MΩ are NOT! –Prefixes Can Result in Exponent Errors  Strategy: Eliminate Prefixes for Complex Calculations  Example: R = 40 kΩ, I = 2 mA

ENGR-43_Lec-02-1_Ohms_Law.ppt 18 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example: i, v, P, R relations  Given Lamp Ckt  Find Lamp Current, I Lamp Resistance, R Charge Supplied to Lamp in 1 minute, Q 1  Use P&v Pwr Rlns  Thus + -   V 12 HALOGEN LAMP WP 60   And

ENGR-43_Lec-02-1_Ohms_Law.ppt 19 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example: q, i, v, P, R  Given Circuit with CHARGE entering at Node-a  2 R a b  Find i ab (t = 1S) v ab (t = πS) P R (t)  Find i(t) from q(t)  Thus

ENGR-43_Lec-02-1_Ohms_Law.ppt 20 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example: i, v, P, R  Next Find v ab (π)  2 R a b  Use v = iR i(t) from Before  Thus  Use the Power Rlns for P R (t)

ENGR-43_Lec-02-1_Ohms_Law.ppt 21 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis WhiteBoard Work  After Example See me to ADD the Class We’ll Review Lab-01 We’ll Perform Lab-01 during Lab-Session Starting at 9am –Pick up Lab Sheet  Also on ENGR43 WebPage  Let’s Work This Problem Find Vs

ENGR-43_Lec-02-1_Ohms_Law.ppt 22 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Power by Passive Sign Convention  When in Doubt, A-B it Using VOLTAGE Polarity as Ref. A B A B A B ABABAB

ENGR-43_Lec-02-1_Ohms_Law.ppt 23 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis

ENGR-43_Lec-02-1_Ohms_Law.ppt 24 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis