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Phasor Relationships for Circuit Elements (7.4)

Phasor Relationships for Circuit Elements (7.4). Dr. S. M. Goodnick September 10, 2003. 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.

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Phasor Relationships for Circuit Elements (7.4)

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  1. Phasor Relationships for Circuit Elements (7.4) Dr. S. M. Goodnick September 10, 2003 ECE201 Lect-7

  2. 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. ECE201 Lect-7

  3. I-V Relationship for a Resistor Suppose that i(t) is a sinusoid: i(t) = IM ej(wt+q) Find v(t) + i(t) v(t) R – ECE201 Lect-7

  4. Computing the Voltage ECE201 Lect-7

  5. Class Example • Learning Extension E7.5 ECE201 Lect-7

  6. 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. ECE201 Lect-7

  7. + i(t) v(t) C – I-V Relationship for a Capacitor Suppose that v(t) is a sinusoid: v(t) = VM ej(wt+q) Find i(t) ECE201 Lect-7

  8. Computing the Current ECE201 Lect-7

  9. Phasor Relationship • Represent v(t) and i(t) as phasors: V = VMq I = jwCV • The derivative in the relationship between v(t) and i(t) becomes a multiplication by jw in the relationship between V and I. ECE201 Lect-7

  10. Example v(t) = 120V cos(377t + 30) C = 2mF • What is V? • What is I? • What is i(t)? ECE201 Lect-7

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

  12. I-V Relationship for an Inductor V = jwLI + i(t) v(t) L – ECE201 Lect-7

  13. Example i(t) = 1mA cos(2p 9.15•107t + 30) L = 1mH • What is I? • What is V? • What is v(t)? ECE201 Lect-7

  14. Class Example • Learning Extension E7.6 ECE201 Lect-7

  15. Circuit Element Phasor Relations(ELI and ICE man) ECE201 Lect-7

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