In this circuit, when the switch is opened at t=0, the current through the inductor gradually decreases over time, causing a voltage to develop across the inductor and a corresponding drop in the voltage across the resistor.
VoltageBased on the given information, we can draw the following circuit diagram:
+-----R-----+
Vs --| |
| +---> vr
| |
+----L-----x--+
|
---
--- ix
|
GND
where
Vs is the voltage source with a value of 18 V, R is the resistor with a value of 12 Ω, L is the inductor with a value of 1 H, ix is the current through the inductor, and vr is the voltage across the resistor.Before the switch is opened at t=0, the circuit is in steady-state, which means that the current through the inductor is constant and there is no voltage across the inductor. When the switch is opened at t=0, the current through the inductor cannot change instantaneously, so it will continue to flow in the same direction but will gradually decrease over time.
As the current decreases, a voltage will develop across the inductor, which will oppose the change in current.
To solve for ix and vr for t>0, we can use the differential equation that describes the behavior of the circuit:
[tex]L(di/dt) + R\times i = Vs[/tex]
where
i is the current through the inductor, di/dt is the rate of change of the current, and Vs is the voltage source.Taking the derivative of both sides with respect to time, we get:
[tex]L(d^2i/dt^2) + R(di/dt) = 0[/tex]
This is a second-order linear homogeneous differential equation with constant coefficients. The characteristic equation is:
[tex]Lr^2 + Rr = 0[/tex]
which has two roots:
r1 = 0r2 = -R/LThe general solution to the differential equation is therefore:
[tex]i(t) = Ae^{(r1t)} + Be^{(r2t)}[/tex]
[tex]= A + Be^{(-R/L\times t)}[/tex]
where
A and B are constants that depend on the initial conditions.
To solve for A and B, we can use the initial conditions at t=0. Before the switch is opened, the current through the inductor is constant, so we have:
[tex]i(0-) = i(0+) = ix[/tex]
After the switch is opened, the voltage across the inductor is zero, so we have:
[tex]vL(0+) = 0[/tex]
Using Ohm's law, we can write:
[tex]vR = iR[/tex]
where
vR is the voltage across the resistor, which is equal to vr.
Therefore, we have:
[tex]vr = iR = (di/dt)\times R[/tex]
Taking the derivative of the equation for i(t), we get:
[tex]di/dt = -B\times (R/L)e^{(-R/Lt)}[/tex]
Using the initial condition vL(0+) = 0, we can write:
[tex]vL = L(di/dt)[/tex]
Substituting in the expression for di/dt and integrating with respect to time, we get:
[tex]vL = -BR/L \times (e^{(-R/L\timest)} - 1)[/tex]
Using the fact that vL = 0 at t=0+, we can solve for B:
B = ix*R/L
Substituting this expression for B into the equation for i(t), we get:
i(t) = ix + (Vs/R - ix)e^(-R/Lt)
This matches the given expression for i(t), so we can confirm that:
A = ixVs/R - ix = BR/LB = ixR/LTo solve for vr, we can use the equation:
[tex]vr = (di/dt)R[/tex]
[tex]vL = -BR/L \times (e^{(-R/L\times t)} - 1)[/tex]
Therefore, in this circuit, when the switch is opened at t=0, the current through the inductor gradually decreases over time, causing a voltage to develop across the inductor and a corresponding drop in the voltage across the resistor.
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Explain why it is better to jump and land with bent knees rather than straight legs? Use key physics vocabulary.
Answer:
Bent knees
Explanation:
Depending the height your jumping from, if you were jumping from a high structure it's best if you jump and land on knees so you dont sprang your ankles from jumping and landing on your straight legs, you could even pull a muscle if you land on straight legs.
There is a scale with a basket on it. A brick, brick #1 is placed on the scale. The brick has a mass of 10 kg. What are the two forces acting on the brick?
Answer:
Weight and reaction.
Explanation:
With respect to Newton's third law of motion, action and reaction have equal magnitude but acts in opposite direction.
Thus, the brick of mass 10 kg has its weight (due to gravitational pull of the earth), which acts downwards through its center of mass. This makes the scale to produce an opposing force of equal magnitude, which acts upwards. These two forces acting in opposite directions balancing each other.
The two forces acting on the brick are: its weight and the reaction from the scale.
uses of electromagnetic wave
20 POINTS! PLZ HELP ME. :-)
Answer:
A
Explanation:
Because both the elements are non-metals
What is another term that refers to foodborne illness?
2x+1-2x=8. solve this problem math
Answer:
x=7
Explanation:
2x+1-2x=8
or,2x-2x=8-1
x=7
Pick all the right ones !!
how does a longshore current affect a beach?
Answer:
"Longshore currents are affected by the velocity and angle of a wave. When a wave breaks at a more acute (steep) angle on a beach, encounters a steeper beach slope, or is very high, longshore currents increase in velocity. ... This process, known as “longshore drift,” can cause significant beach erosion."
Credits to ocean service
Explanation:
Hope this helps
Calculate the momentum of a 1kg box moving at a velocity of 50 m/s.
the momentum = m * v
m : mass
v : velocity
momentum = 1 * 50 = 50 kg.m/s
Urea gets from body cells to the blood plasma by diffusion through the tissue fluid. Explain what this means?
Answer:
Glucose diffuse from the blood plasma, across the capillary walls to the tissue fluid, and then to the cell.
Glucose diffuse from the blood plasma, across the capillary walls to the tissue fluid, and then to the cell. The waste product urea diffuse from the cells of the liver to the tissue fluid, and then across the capillary walls into the blood plasma.
tartaric acid is present in spinach true or false
Answer:
falseExplanation:
because Oxalic acid is present in spinach
MARK ME AS BRAINLISTWho is farther from home at 4 minutes?
Answer:
lil's sister
hope this helps pls mark brainliest
Will clothes dry faster when they are folded or when they are not folded on the line?
Answer:
Not folded
Explanation:
Hello anyone I need the answer to this, thank you!
Answer:
yes
yes yes yes yes
yes yes yes
Where did Ford first see parts made from vanadium steel? What properties of this steel impressed Ford? Did Ford need to overcome any problems before going ahead with his plan?
Explanation:
Historical sources believe that Henry Ford first saw parts made from vanadium steel in Europe which were been used on racing cars and luxurious vehicles.
Ford was impressed due to the fact that Vanadium steel unlike normal steel was cheaper and at the same time stronger and lighter if it was used on automobiles.
An orbiting satellite experiences no force due to the Earth's
gravity.
Answer:
false
Explanation:
The statement "An orbiting satellite experiences no force due to the Earth's gravity." is a False statement. This is further explained below.
What is Gravity?Generally, Gravity is simply defined as the force that pulls items toward the center of a planet or other entity.
In conclusion, an orbiting satellite experiences force due to the Earth's gravity.
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Name some minerals used as gems.
Answer:
Minerals to Gemstones
Mineral Name Gemstone Name
Beryl Aquamarine, Beryl, Bixbite, Emerald, Goshenite, Heliodore, Morganite
Brazilianite Brazilianite
Chalcedony Agate, Aventurine, Bloodstone, Carnelian, Chrysoprase, Heliotrope, Jasper, Onyx, Sard
Chrysoberyl Alexandrite, Chrysoberyl
is the number of paper clips in step 2 the same as the number of paper clips in step 3? why do/don't you think so?
The number of paper clips in step 2 is the same as the number of paper clips in step 3 is a true statement, as the mass is the same for both.
What is mass?It is possible to define every mechanical quantity in terms of mass, length, and time. The SI unit for mass, denoted by the letter m, is the kilogram. While mass is typically thought of as an immutable feature of an item, relativistic mass must be taken into account when traveling at speeds close to the speed of light.
Given:
The mas of the paper clips are the same,
Assume the number of clips in step two is x and the mass is m, the mass in the third step is the same as in step 2,
Thus, the number of clips = Total mass of paper clip / mass of one clip,
The number of clips = m / x
As we can see, if the mass is equal, then the number of clips will also be equal.
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13-1 LIVE
2, A rectangulv Container of base socmby 30cm is filled
with water to be depth of 5cm. how much is the pressure exerted
at the base? (take pw= 1000kg /m3 and g=10m/s)
Correct question is;
2, A rectangular Container of base 50 cm by 30cm is filled with water to be depth of 5cm. how much is the pressure exerted at the base? (take pw= 1000kg /m3 and g=10m/s)
Answer:
P = 500 N/m²
Explanation:
Pressure exerted at the base is the hydrostatic pressure and it is given by the formula;
P = ρgh
Where;
ρ is density = 1000 kg/m³
g = 10 m/s²
h is depth = 5 cm = 0.05 m
Thus;
P = 1000 × 10 × 0.05
P = 500 N/m²
1. A stone is thrown upwards with an initial velocity of 25 m/s at angle of 30° to the ground a. Show that the vertical component if the velocity at the starting is 12.5 m/s upwards.
The vertical component of the velocity at the starting is 12.5 m/s upwards.
What is velocity?Velocity is the direction at which an object is moving and serves as a measure of the rate at which its position is changing as seen from a specific point of view and as measured by a specific unit of time.
In kinematics, the area of classical mechanics that deals with the motion of bodies, velocity is a fundamental idea.
Given that stone is thrown upwards with an initial velocity of 25 m/s at angle of 30°.
Hence, the vertical component of the velocity in upward direction = 25 sin30° m/s
= 25 × 1/2 m/s
= 12.5 m/s.
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Where do electrons spend most of their time?
Answer:
around the nuclei of each atom
Explanation:
Answer:
Before bonding, the atom's electrons spend most of their time around the nuclei of each atom.
Explanation:
Once bonded, the electrons spend most of their time between the two nuclei.
Which of the following waves has the longest wavelength? Group of answer choices a.ultraviolet b.gamma c.visible light d.microwaves
Answer: visible light
Explanation:
An object can have forces acting upon it, but might not accelerate
True
or
False?
Answer:
true
Explanation:
if you apply force to the top of a square it will not move
if the 50 kg object slows down to a velocity of 1 m/s how much kinetic energy does it have 100j 50j 25j or none
[tex]ek = \frac{1}{2}m {v}^{2} [/tex]
[tex]ek = \frac{1}{2}(50) {(1)}^{2} [/tex]
[tex]ek = \frac{1}{2}(50)[/tex]
[tex]ek = 25j[/tex]
//
I'm not really sure but I do know that it's not 0 because the object is still moving, even if it's only moving at 1 m/s.
Why can videos be streamed from one computer to another with excellent quality?
Answer:
(d) they are transmitted using digital signals
Explanation:
i just did the quiz an got it right
Answer:they are transmitted using digital signals
Explanation:
i need help it is psychology
Answer:
C. Forebrain
Explanation:
The Basil Ganglia, sits on the base of the forebrain.
Which of the scientist responsible for cell theory would be the most likely to write a book titled Cells Come from Cells
Answer:
Rudolf Virchow
Explanation:
popularized the cell theory in an 1855 essay entitled “Cellular Pathology.” (b) The idea that all cells originate from other cells was first published in 1852 by his contemporary and former colleague Robert Remak (1815–1865).
Explanation:
Rudolf Virchow
-Rudolf Virchow would be the most likely to write a book titled 'Cells Come From Cells' because in cell theory he added a point that 'All cells arises from pre-existing cells. ' which means that all cells come from another cells which is as similar as the title of the book
The angle between the incident ray and the reflected ray from a mirror is 720.
Find the angle of incidence.
Answer:
when a ray of light is incident normally on a plane mirror the angle between incident and reflected ray is 0 degree or 180 degree
Explanation:
What is the volume of the water in the graduated cylinder gizmo Student Volume Lab Sheet (cm3 and mL)
Answer:
The volume of water in the graduated cylinder will be equal to the calculated volume of the sphere.
Explanation:
The volume of solid objects can be measured by completely immersing these solids in an overflow faucet filled to brim with a liquid in which the solid does not dissolve. This is known as the displacement method. When water is used, it is known as water displacement method.
In the Volume Lab Sheet, a sphere whose volume has been pre-calculated is immersed in the overflow faucet containing water. The displaced water is collected in a beaker and the volume is obtained using a 50 mL measuring cylinder.
The volume of a sphere is calculated using the following formula:
Vsphere = 4πr³/ 3
The symbol π represents the number pi, which is about 3.14. The letter r stands for the radius of the sphere, which is the distance from the center of a sphere to its surface. The radius is exactly half of the diameter, which is the distance across the sphere through its center.
The volume of the water in the measuring cylinder is found to be equal to the calculated volume of the sphere. This is because an object immersed completely in a liquid displaces a volume of liquid equal to its own volume.
pls help i’ll give brainliest if you give a correct answer!!
Answer:
South ....................
Answer:
South ;)
Explanation:
I just did it .