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

2. Mirror Image

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

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 Resistors in PARALLEL

5. 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

6. 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

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. 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

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 Resistors in PARALLEL

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

14. Inductor Ladder Network
Find Leq for Li = 4 mH
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. 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