EE233 Summer 2015 Department of Electrical Engineering University of Washington EE233 Homework 4 July 11, 2015 Due Date: July 20, 2015 HW4 Topics: • Average Power • Power Factor • Maximum Power Transfer • Complex Power • RMS power and current HW4 Referenc

EE233 Summer 2015 Department of Electrical Engineering University of Washington

EE233 Homework 4

July 11, 2015

Due Date: July 20, 2015

HW4 Topics:

• Average Power

• Power Factor

• Maximum Power Transfer

• Complex Power

• RMS power and current

HW4 References:

• Textbook section 10.1 − 10.6

1. (Average Power) Find the average power absorbed by each resistor and each source. Hint: The circuit is in steady state, use superposition to solve this problem.

+ −100V

1kΩ

1µF 1kΩ 0.2 cos 2000tA

2. (Power Factor) Find the power factor.

(a) A load consisting of a series connection of a 50Ω resistor and a 10µF capacitor operating at 60Hz.

10µF 50Ω

(b) A load that is capacitive and requires 40A RMS and 8kW at 220V RMS.

3. (Complex Power) Use the method of Complex Power to compute the power factor if the load is one consisting of 5kW load at a power factor of 0.85 leading connected in parallel with a 10kW load at a power factor of 0.95 lagging.

EE233 Summer 2015 Department of Electrical Engineering University of Washington

Z1 Z2I1 I2

4. (Average Power) Find the average power, reactive power, complex power, and apparent power absorbed by the load (resistor and capacitor in series) if ig(t) = 50 cos 2000t mA.

ig 2mH 20nF

5kΩ

5. (Maximum Power) Let vg(t) = 100 cos (4000t) V.

vg

8mH

40Ω

5µF

ZL

b

a

(a) Compute the Thevenin equivalent circuit of terminals a − b. (b) If we want to have maximum power, what is the load ZL.

(c) Compute the maximum average power delivered to the load.

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