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Bridge circuits

Circuits having the form of [link] are termed bridge circuits .

  1. What resistance does the current source see when nothing is connected to the output terminals?
  2. What resistor values, if any, will result in a zero voltage for v out ?
  3. Assume R 1 , R 2 , R 3 and R 4 . Find the current i when the current source i in is 4 2 2 20 t . Express your answer as a sinusoid.

Cartesian to polar conversion

Convert the following expressions into polar form. Plot their location in the complex plane .

  1. 1 -3 2
  2. 3 4
  3. 2 6 3 2 6 3
  4. 4 3 1 1 2
  5. 3 4 2
  6. 3 2 2 4
  7. 3 1 3

The complex plane

The complex variable z is related to the real variable u according to z 1 u

  • Sketch the contour of values z takes on in the complex plane.
  • What are the maximum and minimum values attainable by z ?
  • Sketch the contour the rational function z 1 z 1 traces in the complex plane.

Cool curves

In the following expressions, the variable x runs from zero to infinity. What geometric shapes do the following trace in the complex plane?

  1. x
  2. 1 x
  3. x x
  4. x x 4

Trigonometric identities and complex exponentials

Show the following trigonometric identities using complex exponentials. In many cases, they were derived using this approach.

  1. 2 u 2 u u
  2. u 2 1 2 u 2
  3. u 2 u 2 1
  4. u u u

Transfer functions

Find the transfer function relating the complex amplitudes of the indicated variable and thesource shown in [link] . Plot the magnitude and phase of the transferfunction.

Circuit a

Circuit b

Circuit c

Circuit d

Using impedances

Find the differential equation relating the indicated variable to the source(s) using impedances for each circuitshown in [link] .

Circuit a

Circuit b

Circuit c

Circuit d

Measurement chaos

The following simple circuit was constructed but the signal measurements were made haphazardly. When the source was 2 f 0 t , the current i t equaled 2 3 2 f 0 t 4 and the voltage v 2 t 1 3 2 f 0 t .

  1. What is the voltage v 1 t ?
  2. Find the impedances Z 1 and Z 2 .
  3. Construct these impedances from elementary circuit elements.

Transfer functions

In the following circuit , the voltage source equals v in t 10 t 2 .

  1. Find the transfer function between the source and the indicated output voltage.
  2. For the given source, find the output voltage.

A simple circuit

You are given this simple circuit .

  1. What is the transfer function between the source and the indicated output current?
  2. If the output current is measured to be 2 t , what was the source?

Circuit design

  1. Find the transfer function between the input and the output voltages for the circuits shown in [link] .
  2. At what frequency does the transfer function have a phase shift of zero? What is the circuit's gain atthis frequency?
  3. Specifications demand that this circuit have an output impedance (its equivalent impedance) less than 8Ωfor frequencies above 1 kHz, the frequency at which the transfer function is maximum. Find element valuesthat satisfy this criterion.

Equivalent circuits and power

Suppose we have an arbitrary circuit of resistors that we collapse into an equivalent resistor using the series and parallel rules. Is the power dissipated by the equivalent resistor equal to the sum of the powers dissipated by the actual resistors comprising the circuit?Let's start with simple cases and build up to a complete proof.

  1. Suppose resistors R 1 and R 2 are connected in parallel. Show that the power dissipated by R 1 R 1 equals the sum of the powers dissipated by the component resistors.
  2. Now suppose R 1 and R 2 are connected in series. Show the sameresult for this combination.
  3. Use these two results to prove the general result we seek.

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
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John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
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emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
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Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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Source:  OpenStax, Fundamentals of electrical engineering i. OpenStax CNX. Aug 06, 2008 Download for free at http://legacy.cnx.org/content/col10040/1.9
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