For each circuit shown in
[link] , the current
$i$ equals
$\cos (2\pi t)$ .
What is the voltage across each element and what is the voltage
$v$ in each case?
For the last circuit, are there element values that make the voltage
$v$ equal zero for all time?
If so, what element values work?
Again, for the last circuit, if zero voltage were possible, what circuit element could substitute for the capacitor-inductor series combination that would yield the same voltage?
Solving simple circuits
Write the set of equations that govern
Circuit A's behavior.
Solve these equations for
${i}_{1}()$ :
In other words, express this current in terms ofelement and source values by eliminating non-source
voltages and currents.
For Circuit B, find the value for
${R}_{\text{L}}$ that results in a current of 5 A passing through
it.
What is the power dissipated by the load resistor
${R}_{\text{L}}$ in this case?
Equivalent resistance
For
each of the
following
circuits , find the equivalent resistance using
series and parallel combination rules.
Calculate the conductance seen at the terminals for
circuit (c) in terms of each element's conductance.Compare this equivalent conductance formula with the
equivalent resistance formula you found for circuit (b).How is the circuit (c) derived from circuit (b)?
Superposition principle
One of the most important consequences of circuit laws
is the
Superposition Principle : The current
or voltage defined for any element equals the sum of thecurrents or voltages produced in the element by the
independent sources. This Principle has importantconsequences in simplifying the calculation of ciruit
variables in multiple source circuits.
For the
depicted circuit , find the
indicated current using any technique you like (youshould use the simplest).
You should have found that the current
$i$ is a linear combination of the two source values:
$i={C}_{1}(){v}_{\mathrm{in}}()+{C}_{2}(){i}_{\mathrm{in}}()$ .
This result means that we can think of the current asa superposition of two components, each of which is
due to a source. We can find each component by settingthe other sources to zero. Thus, to find the voltage
source component, you can set the current source tozero (an open circuit) and use the usual tricks. To
find the current source component, you would set thevoltage source to zero (a short circuit) and find the
resulting current. Calculate the total current
$i$ using the
Superposition Principle. Is applying the SuperpositionPrinciple easier than the technique you used in part
(1)?
Current and voltage divider
Use current or voltage divider rules to calculate the
indicated circuit variables in
[link] .
Thévenin and mayer-norton equivalents
Find the Thévenin and Mayer-Norton equivalentcircuits for the
following circuits .
Detective work
In the
depicted
circuit , the circuit
${N}_{1}()$ has the v-i relation
${v}_{1}()=3{i}_{1}()+7$ when
${i}_{s}()=2$ .
Find the Thévenin equivalent circuit for
circuit
${N}_{2}()$ .
With
${i}_{s}()=2$ ,
determine
$R$ such that
${i}_{1}()=-1$ .
Questions & Answers
Is there any normative that regulates the use of silver nanoparticles?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?