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Electronics Homework: Determining Reactance, Time Constants, and Analyzing Circuits - Prof, Assignments of Physics

Dr. Sohl's electronics homework #2 for phys 3410, including problems on determining reactance for capacitors and inductors at different frequencies, calculating time constants for charging circuits, analyzing rlc circuits, and working with complex numbers. Students are required to show their work to receive credit.

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Pre 2010

Uploaded on 07/22/2009

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PHYS 3410 Electronics, Dr. Sohl
Homework #2, 50 pts.
Do your w ork on a sep arate sheet o f paper. Circ le your answers . You must show your work to get credit. Fact of Life: If you
write like a slob, people (like your future bosses) will think you are a slob. (Selected answers are given in [ ] brackets.)
1. (4 pts) Determine the reactance for a 0.1 ìF capacitor when connected to ac voltage with a
frequency of (a) 60 Hz, (b) 1.0 kHz.
2. (4 pts) Determine the reactance for a 180 ìH inductor when connected to ac voltage with a
frequency of (a) 60 Hz, (b) 1.0 kHz.
3. (3 pts) Determine the time constant for a 12V DC circuit that is charging a 470 ìF capacitor in
series with a 10 k resistor.
4. (3 pts) Determine the time constant for a 12V DC circuit that
is forcing current through a 3.5 mH inductor in series with a
680 Ù resistor.
For problems 5 & 6, express complex results in exponential form.
5. (12 pts) Analyze the circuit shown on the right.
(a) Determine the complex current out of the supply.
OUT
(b) Determine the complex voltage out, V.
OUT
(c) What is the phase shift of V relative to V1? [-41.5E]
(d) Is this a high pass or low pass filter? What is the cuttoff
frequency? [1100 Hz]
6. (12 pts) Analyze the circuit shown on the right.
(a) Determine the complex current out of the supply.
OUT
(b) Determine the complex voltage out, V.
OUT
(c) What is the phase shift of V relative to V1? [48.5E]
(d) Is this a high pass or low pass filter? What is the cutoff
frequency? [1100 Hz]
7. (12 pts) Analyze the RLC circuit shown below. All phases are relative to the input voltage.
(a) Determine the complex voltage amplitude and phase across the inductor. [76.7V, 165.3E]
(b) Determine the complex voltage amplitude and phase across the capacitor. [88.3V, -14.7E]
(c) Determine the complex voltage amplitude and phase across the resistor. [3.1V, 75.3E]
(d) At a given instant of time (use t=0 for ease) what is the sum of the real voltages across the
three components?
Note that there are more problems on the next page...
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PHYS 3410 Electronics, Dr. Sohl

Homework #2, 50 pts.

Do your work on a separate sheet of paper. Circle your answers. You must show your work to get credit. Fact of Life: If you write like a slob, people (like your future bosses) will think you are a slob. (Selected answers are given in [ ] brackets.)

  1. (4 pts) Determine the reactance for a 0.1 ìF capacitor when connected to ac voltage with a frequency of (a) 60 Hz, (b) 1.0 kHz.
  2. (4 pts) Determine the reactance for a 180 ìH inductor when connected to ac voltage with a frequency of (a) 60 Hz, (b) 1.0 kHz.
  3. (3 pts) Determine the time constant for a 12V DC circuit that is charging a 470 ìF capacitor in series with a 10 k resistor.
  4. (3 pts) Determine the time constant for a 12V DC circuit that is forcing current through a 3.5 mH inductor in series with a 680 Ù resistor.

For problems 5 & 6, express complex results in exponential form.

  1. (12 pts) Analyze the circuit shown on the right. (a) Determine the complex current out of the supply. (b) Determine the complex voltage out, V OUT. (c) What is the phase shift of V OUT relative to V1? [-41.5E] (d) Is this a high pass or low pass filter? What is the cuttoff frequency? [1100 Hz]
  2. (12 pts) Analyze the circuit shown on the right. (a) Determine the complex current out of the supply. (b) Determine the complex voltage out, V OUT. (c) What is the phase shift of V OUT relative to V1? [48.5E] (d) Is this a high pass or low pass filter? What is the cutoff frequency? [1100 Hz]
  3. (12 pts) Analyze the RLC circuit shown below. All phases are relative to the input voltage. (a) Determine the complex voltage amplitude and phase across the inductor. [76.7V, 165.3E] (b) Determine the complex voltage amplitude and phase across the capacitor. [88.3V, -14.7E] (c) Determine the complex voltage amplitude and phase across the resistor. [3.1V, 75.3E] (d) At a given instant of time (use t =0 for ease) what is the sum of the real voltages across the three components?

Note that there are more problems on the next page...

The following problems are for your practice only. The solutions will be posted. If you are very confident with working with complex numbers then don’t bother. If you are not sure you would do OK with these problems on the test then you should work through them and check your answers against the key.

  1. Show that r cosè = r ( e jè^ + e -jè)/2. (Note, this is one of Euler’s identities.)
  2. Conversion of complex numbers. Convert each of the following complex numbers into the two other representations of a complex number (x + jy, r(cosè + j sinè), and r e jè). (a) 3 + j4 (b) (c) 3(cos 60E + j sin 60E).
  3. Addition and subration of complex numbers. Calculate each of the following complex numbers. (a) (3 + j 4) + (-3 + j 3) (b) 3 e j 60E^ - 4 e j30E
  4. Products of complex numbers. Calculate the products of each of the following complex numbers. (a) (3 + j 4) (-3 + j 3) (b) 3 e j 60E^4 e j30E^ (c) (2 + j 6)^2
  5. Quotients of complex numbers. Calculate the quotients of each of the following complex numbers. (a) (3 + j 4) / (-3 + j 3) (b) 3 e j 60E^ / 4 e j30E