Chapter 6 – Inductance, Capacitance and Mutual Inductance

1. Chapter 6 – Inductance, Capacitance and Mutual Inductance https://qph.ec.quoracdn.net/main-qimg-90dbafd7084f2614f3b3c6e6c6600edf-c Terminology Inductors Capacitors Series/Parallel Inductors and Capacitors Mutual Inductance http://www.insidesocal.com/tomhoffarth/files/2015/10/MutualInductance.png https://www.build-electronic-circuits.com/wp-content/uploads/2013/05/electrolytic-capacitor.jpg

2. Terminology Inductance– Relates the induced voltage to the current Capacitance – Relates the displacement current to the voltage Passive Elements – cannot generate energy Mutual Inductance– The voltage induced in one circuit that is related to The time varying current in another circuit.

3. The Inductor v = volts L = inductance (in Henrys) i = amperes t =in seconds Inductors store energy in terms of an electrical field

4. The Inductor If current is constant, the voltage across the ideal inductor is zero, making The inductor behave like a short in the presence of a constant or DC current. Current cannot change instantaneously in an inductor, it would require an infinite voltage which is not possible. Inductors block AC and allow DC to flow

5. The Inductor Example: The independent current source shown generates zero current for t < 0 and a pulse A for t > 0. Sketch the current waveform. At what instant of time is the current Maximum Maximum occurs when the derivative is zero

6. The Inductor C) Express the voltage across the terminals of the 100 mH inductor as a function of time. D) Sketch the voltage waveform

7. The Inductor Current in terms of voltage: Integrate the left side only Multiply both sides by the differential of time In most practical applications Re-Write so solving Is more convenient

8. The Inductor Determine current given voltage Example: The voltage pulse applied to the 100mH inductor is 0 for t<0 and for t >0. Sketch the voltages as a function of time. Find the inductor current as a function of time. Sketch the current as a function of time. Max when

9. The Inductor b) Find the inductor current as a function of time. c) Sketch the current as a function of time. Place the equation into your calculator. Use the integral table on pg 759 Appendix G

10. The Inductor Power and energy in the inductor: In terms of voltage In terms of current In terms of energy

11. The Inductor Example: Determine plots of I, v, p, and w versus time. Done in previous example Done in previous example Joules

12. The Inductor Example: In what time interval is energy being stored in the inductor? From 0 to 0.2s, also corresponds to p>0 In what time interval is energy being extracted from the inductor? From 0.2s to ∞, also corresponds to p<0 What is the maximum energy stored in the inductor? From previous example maximum current is 0.736A

13. The Inductor Example: Evaluate the integrals of power. From before: Use a larger number like 100 to evaluate In your calculator Use your calculator to save time Use your calculator to save time Energy Stored Energy Extracted After current peaks, no energy is store in the inductor

14. The Capacitor i in Amperes C in Farads V in Volts t in seconds Capacitors store electric charge Passive sign convention

15. The Capacitor Voltage cannot change instantaneously across the terminals of a capacitor or it would produce infinite current If voltage across the terminals is constant, the capacitor current is zero, because a conduction current cannot be established in the dielectric material. It must have a time varying voltage to operate Therefore a capacitor acts like an open circuit in the presence of a constant voltage AC can pass through better, but a capacitor does not block DC.

16. The Capacitor In terms of voltage For simplicity

17. The Capacitor In terms of power Substitute Alternatively: V calculated previously

18. The Capacitor In terms of energy Integrate Energy in Joules

19. The Capacitor Example: The voltage pulse described by the following equations is impressed across the terminals of a Capacitor Derive the expressions for the capacitor current: Take the derivative of each voltage with respect to time

20. The Capacitor Example: The voltage pulse described by the following equations is impressed across the terminals of a Capacitor Previously calculated Derive the expressions for the power: Substitute in for v and i

21. The Capacitor Example: The voltage pulse described by the following equations is impressed across the terminals of a Capacitor Derive the expressions for the energy: Substitute in for C and v

22. The Capacitor Example: The voltage pulse described by the following equations is impressed across the terminals of a Capacitor Sketch the voltage, current, power, and energy as functions of time:

23. The Capacitor Example: Specify the interval of time when energy is being stored in the capacitor. Specify the interval of time when energy is delivered by the capacitor.

24. The Capacitor Example: Evaluate the integrals for the capacitors energy Use a larger value to replace infinity Use your calculator for the derivatives

25. Series-Parallel Combinations of Inductance and Capacitance Inductors in Series Inductors in Parallel

26. Series-Parallel Combinations of Inductance and Capacitance Capacitors in Series Capacitors in Parallel