1. ECE201 Lect-71 Phasor Relationships for Circuit Elements (7.4) Dr. S. M. Goodnick September 10, 2003

2. ECE201 Lect-72 Phasor Relationships for Circuit Elements Phasors allow us to express current-voltage relationships for inductors and capacitors much like we express the current-voltage relationship for a resistor. A complex exponential is the mathematical tool needed to obtain this relationship.

3. ECE201 Lect-73 I-V Relationship for a Resistor Suppose that i(t) is a sinusoid: i(t) = I M e j(  t+  Find v(t) R v(t) + – i(t)

4. ECE201 Lect-74 Computing the Voltage

5. ECE201 Lect-75 Class Example Learning Extension E7.5

6. ECE201 Lect-76 Energy Storage Elements Capacitors store energy in an electric field. Inductors store energy in a magnetic field. Capacitors and inductors are passive elements: –Can store energy supplied by circuit –Can return stored energy to circuit –Cannot supply more energy to circuit than is stored.

7. ECE201 Lect-77 I-V Relationship for a Capacitor Suppose that v(t) is a sinusoid: v(t) = V M e j(  t+  Find i(t) C v(t) + – i(t)

8. ECE201 Lect-78 Computing the Current

9. ECE201 Lect-79 Phasor Relationship Represent v(t) and i(t) as phasors: V = V M   I = j  C V The derivative in the relationship between v(t) and i(t) becomes a multiplication by j  in the relationship between V and I.

10. ECE201 Lect-710 Example v(t) = 120V cos(377t + 30  ) C = 2  F What is V? What is I? What is i(t)?

11. ECE201 Lect-711 Class Example Learning Extension E7.7

12. ECE201 Lect-712 I-V Relationship for an Inductor V = j  L I L v(t) + – i(t)

13. ECE201 Lect-713 Example i(t) = 1  A cos(2  9.1510 7 t + 30  ) L = 1  H What is I? What is V? What is v(t)?

14. ECE201 Lect-714 Class Example Learning Extension E7.6

15. ECE201 Lect-715 Circuit Element Phasor Relations (ELI and ICE man)