ECE 3600 Homework # 2

c ECE 3600 homework # 2 1. Express the impedance of a 5.2mH inductor at 60 Hz in polar form. 2. A capacitor impedance has a magnitude of 240Ω at a frequency of 1.8kHz . What is the value of capacitor? 3. Find Zeq in each case. a) b) R .330 Ω

R .330 Ω V( )jω

V( )jω ..10 V ej0 ..10 V ej0 C .0.22 µF

f .1 kHz L .100 mH f .2 kHz c)

V( )jω L .160 mH C .0.03 µF

..8 V ej0 R .4 kΩ

f .1.5 kHz 4. Find the current I (jω) in each case above. 5. a) Find Z . Hint: Find the total impedance (R+Z) first. i( )t = ..30 mA cos( ).ω t .36 deg b) Which leads, current or voltage? R .180 Ωω 377

Z = ? v s( )t =

..14 V cos( ).ω t .16 deg c) By how much? I.E. what is the phase angle between the voltage and current? 6. The phasor diagram at right shows the voltage and current in the circuit below

V s .( )60 .j 28 V

Assume the load consists of a resistor in series with a reactive component and the frequency is 60 Hz.V s a) What is the magnitude of the impedance? b) What is the value of the resistor? I ..3.4 A e ..j 30 deg c) What is the reactive component (type and value)? 7. a) Find the AC current source, Iin in polar form. Z 1 .( )120 .90 j Ω b) Find VT.

Z 1 V 1 .9 V c) Choose one:

V T i) The source current leads the source voltage. ii) The source current lags the source voltage. I in Z 2 Z2 = 75 / 30o Ω

Z 2 ..75 Ω e

..j 30 deg ECE 3600 homework # 2 p.1

ECE 3600 homework # 2 p.2 8. a) Find Z1. I T

.( )54 .8 j mA I 1 I2 = 45 / 20o mA b) To make Z1 in the simplest way, what part(s)

would you need? Just determine the needed part(s) from the list below and state why you made that choice, don't find the values. Z2 = 100 / -30o Ω resistor capacitor inductor power supply current source Thevenin resistor Ideal transformer voltmeter ammeter scope c) Choose one: i) I2 leads the source voltage (Vin) ii) I2 lags the source voltage (Vin) d) Choose one: i) I1 leads I2 ii) I1 lags I2 9. Find Z. I T ..423 mA e ..j 105 deg .200 Ω

V s ..100 V e

..j 90 deg ..200 j Ω

Z .1 kΩ

Answers 1. 1.96 Ω /90o 2. .0.368 µF 3. a) .( )330 .628.3 j Ω = 709.7Ω /62.29o b) .( )330 .361.7 j Ω = 489.6Ω /-47.63o c) 1.82kΩ /-15.2o 4. a) .( )6.6 .12.5 j mA = 14.1mA /-62.29o b) .( )13.8 .15.1 j mA = 20.4mA /47.63o c) 4.4mA /15.2o 5. a) 259 .160 j b) The current leads the voltage c) 20o 6. a) .19.5 Ω b) .11.2 Ω c) inductor .42.3 mH 7. a) 60 / 36.87o mA b) 11.54 / 21o V c) i) 8. a) 172 / 53.4o Ω b) phase angle > 0, resistor and inductor c) i) d) ii) 9. 657 Ω /67.4o ECE 3600 homework # 2 p.2