Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Engineering 43 Chp 6.3 Caps & Inds Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu

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Ideal vs Real Practical Elements “Leak” Thru Unwanted Resistance Ideal C & L

Capacitors in Series By KVL for 1-LOOP ckt If the vi(t0) = 0, Then Discern the Equivalent Series Capacitance, CS CAPS in SERIES Combine as Resistors in PARALLEL

Example Find Spot Caps in Series Or Can Reduce Two at a Time Equivalent C Initial Voltage Spot Caps in Series Or Can Reduce Two at a Time Use KVL for Initial Voltage This is the Algebraic Sum of the Initial Voltages Polarity is Set by the Reference Directions noted in the Diagram

Numerical Example Two charged Capacitors Are Connected As Shown. Find the Unknown Capacitance Recognize SINGLE Loop Ckt → Same Current in Both Caps Thus Both Caps Accumulate the SAME Charge And Find VC by KVL VC = 12V-8V = 4V Finally Find C by Charge Eqn

Capacitors in Parallel By KCL for 1-NODE ckt Thus The Equivalent Parallel Capacitance CAPS in Parallel Combine as Resistors in SERIES

Complex Example → Find Ceq

Student Exercise Let’s Turn on the Lites for a Few Minutes To allow YOU to Solve the Problem at Right Find Ceq 4 μF 4 μF 4 μF 4 μF Ceq 4 μF

Find Ceq for Ci = 4 µF

Inductors in Series By KVL For –LOOP ckt Thus Use The Inductance Law INDUCTORS in Series add as Resistors in SERIES

Inductors in Parallel By KCL for 1-NODE ckt And Thus INDUCTORS in Parallel combine as Resistors in PARALLEL

Example – Find: Leq, i0 Series↔Parallel Summary INDUCTORS Combine as do RESISTORS CAPACITORS Combine as do CONDUCTORS

Inductor Ladder Network Find Leq for Li = 4 mH Place Nodes In Chosen Locations Connect Between Nodes When in Doubt, ReDraw Select Nodes

Find Leq for Li = 6mH ReDraw The Ckt for Enhanced Clarity Nodes Can have Complex Shapes The Electrical Diagram Does NOT have to Follow the Physical Layout It’s Simple Now

Summary  C & L Dual Relns

See ENGR-44_Lec-05-1_Capacitors_Prob5-51_5-59.ppt WhiteBoard Work Let’s Work Problems These Problems See ENGR-44_Lec-05-1_Capacitors_Prob5-51_5-59.ppt