Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

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

2. Mirror Image

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

4. 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 Resistorsin PARALLEL

5. Find Equivalent C Initial Voltage Example • 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

6. Two charged Capacitors Are Connected As Shown. Find the Unknown Capacitance Numerical Example • 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

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

8. Complex Example → Find Ceq

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

10. Find Ceq for Ci = 4 µF

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

12. Inductors in Parallel • By KCL for 1-NODE ckt • And • Thus • INDUCTORS in Parallel combine as Resistorsin PARALLEL

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

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

15. 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

16. Summary  C & L Dual Relns

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