1. ECE 201 Circuit Theory I1 Instantaneous Power

2. ECE 201 Circuit Theory I2 Reference for t = 0 Call t = 0 when the current is passing through a positive maximum. Re-write the equations as

3. ECE 201 Circuit Theory I3 Re-writing

4. ECE 201 Circuit Theory I4

5. 5

6. 6 p is at twice the frequency of v and i p is negative over part of the cycle, even though the elements are passive

7. ECE 201 Circuit Theory I7 Average and Reactive Power Average, or Real Power Reactive Power

8. ECE 201 Circuit Theory I8 Power for Purely Resistive Circuits For a purely resistive circuit, the voltage and current are in phase.

9. ECE 201 Circuit Theory I9 Plot of the instantaneous Real Power

10. ECE 201 Circuit Theory I10 Power for Purely Inductive Circuits Voltage and Current are out of phase by 90°. The current lags the voltage by 90°.

11. ECE 201 Circuit Theory I11 Plot of Reactive Power (vars)

12. ECE 201 Circuit Theory I12 Power for Purely Capacitive Circuits Voltage and Current out of phase by 90° The current leads the voltage by 90°.

13. ECE 201 Circuit Theory I13 Plot of Reactive Power (vars)

14. ECE 201 Circuit Theory I14 Power Factor Power factor angle Power factor Reactive factor

15. ECE 201 Circuit Theory I15 Power Factor (continued) Lagging power factor –Current Lags the Voltage –Inductive Load Leading power factor –Current Leads the Voltage –Capacitive Load