Circuits having the form of
[link] are termed
bridge circuits .
What resistance does the current source see when nothing is connected to the output terminals?
What resistor values, if any, will result in a zero voltage for
?
Assume
,
,
and
.
Find the current
when the current source
is
.
Express your answer as a sinusoid.
Cartesian to polar conversion
Convert the following expressions into polar form. Plot
their location in the
complex plane .
The complex plane
The complex variable
is related to the real variable
according to
Sketch the contour of values
takes on in the complex plane.
What are the maximum and minimum values attainable by
?
Sketch the contour the rational function
traces in the complex plane.
Cool curves
In the following expressions, the variable
runs from zero to infinity.
What geometric shapes do the following trace in the complex plane?
Trigonometric identities and complex exponentials
Show the following trigonometric identities using complex exponentials.
In many cases, they were derived using this approach.
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.
Using impedances
Find the differential equation relating the indicated
variable to the source(s) using impedances for each circuitshown in
[link] .
Measurement chaos
The
following simple circuit was constructed but the signal measurements were made haphazardly.
When the source was
, the current
equaled
and the voltage
.
What is the voltage
?
Find the impedances
and
.
Construct these impedances from elementary circuit elements.
What is the transfer function between the source
and the indicated output current?
If the output current is measured to be
, what was the source?
Circuit design
Find the transfer function between the input and the
output voltages for the circuits shown in
[link] .
At what frequency does the transfer function have a
phase shift of zero? What is the circuit's gain atthis frequency?
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.
Suppose resistors
and
are connected in parallel.
Show that the power dissipated by
equals the sum of the powers dissipated by the component resistors.
Now suppose
and
are connected in series.
Show the sameresult for this combination.
Use these two results to prove the general result we seek.
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
from theory: distance [miles] = speed [mph] × time [hours]
info #1
speed_Dennis × 1.5 = speed_Wayne × 2
=> speed_Wayne = 0.75 × speed_Dennis (i)
info #2
speed_Dennis = speed_Wayne + 7 [mph] (ii)
use (i) in (ii) => [...]
speed_Dennis = 28 mph
speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5.
Substituting the first equation into the second:
W * 2 = (W + 7) * 1.5
W * 2 = W * 1.5 + 7 * 1.5
0.5 * W = 7 * 1.5
W = 7 * 3 or 21
W is 21
D = W + 7
D = 21 + 7
D = 28
Salma
Devon is 32 32 years older than his son, Milan. The sum of both their ages is 54 54. Using the variables d d and m m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
however, may I ask you some questions about Algarba?
Amoon
hi
Enock
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67.
Check:
Sales = 3542
Commission 12%=425.04
Pay = 500 + 425.04 = 925.04.
925.04 > 925.00
Munster
difference between rational and irrational numbers
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?