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Cerrena [4.2K]
3 years ago
13

Now solve the differential equation V(t)=−CRdV(t)dt for the initial conditions given in the problem introduction to find the vol

tage as a function of time for any time t. Express your answer in terms of q0, C, R, and t.
Physics
1 answer:
mina [271]3 years ago
8 0

Answer:

V(t) = (q0/C) * e^(−t/RC )

Explanation:

If there were a battery in the circuit with EMF  E , the equation for  V(t)  would be  V(t)=E−(RC)(dV(t)/dt) . This differential equation is no longer homogeneous in  V(t)  (homogeneous means that if you multiply any solution by a constant it is still a solution). However, it can be solved simply by the substitution  Vb(t)=V(t)−E . The effect of this substitution is to eliminate the  E  term and yield an equation for  Vb(t)  that is identical to the equation you solved for  V(t) . If a battery is added, the initial condition is usually that the capacitor has zero charge at time  t=0 . The solution under these conditions will look like  V(t)=E(1−e−t/(RC)) . This solution implies that the voltage across the capacitor is zero at time  t=0  (since the capacitor was uncharged then) and rises asymptotically to  E  (with the result that current essentially stops flowing through the circuit).

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A football is kicked into the air from an initial height of 4 feet. The height, in feet, of the football above the ground is giv
kakasveta [241]

Answer: 0.5 seconds or 2.625 seconds

Explanation:

At t = 0, The ball is 4 ft above the ground.

The height of the football varies with time in the following way:

s(t) = -16 t² + 50 t + 4

we need to find the time in which the height would of the football would be 25 ft:

⇒25 = -16 t² + 50 t + 4

we need to solve the quadratic equation:

⇒ 16 t² - 50 t + 21 = 0

t = \frac{50 \pm \sqrt{50^2-4\times 16\times 21}}{2\times16}

⇒ t = 0.5 s or 2.625 s

Therefore, at t = 0.5 s or 2.625 s, the football would be 25 ft above the ground.

3 0
3 years ago
Read 2 more answers
To collect quantitative data, scientists use all of the following except _____.
Leto [7]
You would use all of the following except for 3. descriptive categories because, that is a qualitative observation using descriptions and not a quantitative observation using numbers.<span />
3 0
3 years ago
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What is the number of protons in the nucleus of an element called?
slava [35]

Answer:

The number of protons within the nucleus of a given atom is equal to the atomic number of the corresponding element, which can be found on the periodic table. For example, the atomic number of helium is two. Therefore, the number of protons is also two

Explanation:

Step 1 - Gather Information

The first thing you will need to do is find some information about your element. Go to the Periodic Table of Elements and click on your element. If it makes things easier, you can select your element from an alphabetical listing.

Use the Table of Elements to find your element's atomic number and atomic weight. The atomic number is the number located in the upper left corner and the atomic weight is the number located on the bottom, as in this example for krypton:

Krypton's data from the Table of Elements

Step 2 - The Number of Protons is...

The atomic number is the number of protons in an atom of an element. In our example, krypton's atomic number is 36. This tells us that an atom of krypton has 36 protons in its nucleus.

The interesting thing here is that every atom of krypton contains 36 protons. If an atom doesn't have 36 protons, it can't be an atom of krypton. Adding or removing protons from the nucleus of an atom creates a different element. For example, removing one proton from an atom of krypton creates an atom of bromine.

Step 3 - The Number of Electrons is...

By definition, atoms have no overall electrical charge. That means that there must be a balance between the positively charged protons and the negatively charged electrons. Atoms must have equal numbers of protons and electrons. In our example, an atom of krypton must contain 36 electrons since it contains 36 protons.

Electrons are arranged around atoms in a special way. If you need to know how the electrons are arranged around an atom, take a look at the 'How do I read an electron configuration table?' page.

An atom can gain or lose electrons, becoming what is known as an ion. An ion is nothing more than an electrically charged atom. Adding or removing electrons from an atom does not change which element it is, just its net charge.

For example, removing an electron from an atom of krypton forms a krypton ion, which is usually written as Kr+. The plus sign means that this is a positively charged ion. It is positively charged because a negatively charged electron was removed from the atom. The 35 remaining electrons were outnumbered by the 36 positively charged protons, resulting in a charge of +1.

Step 4 - The Number of Neutrons is...

The atomic weight is basically a measurement of the total number of particles in an atom's nucleus. In reality, it isn't that clean cut. The atomic weight is actually a weighted average of all of the naturally occurring isotopes of an element relative to the mass of carbon-12. Didn't understand that? Doesn't matter. All you really need to find is something called the mass number. Unfortunately, the mass number isn't listed on the Table of Elements. Happily, to find the mass number, all you need to do is round the atomic weight to the nearest whole number. In our example, krypton's mass number is 84 since its atomic weight, 83.80, rounds up to 84.

The mass number is a count of the number of particles in an atom's nucleus. Remember that the nucleus is made up of protons and neutrons. So, if we want, we can write:

Mass Number = (Number of Protons) + (Number of Neutrons)

For krypton, this equation becomes:

84 = (Number of Protons) + (Number of Neutrons)

If we only knew how many protons krypton has, we could figure out how many neutrons it has. Wait a minute... We do know how many protons krypton has! We did that back in Step 2! The atomic number (36) is the number of protons in krypton. Putting this into the equation, we get:

84 = 36 + (Number of Neutrons)

What number added to 36 makes 84? Hopefully, you said 48. That is the number of neutrons in an atom of krypton.

The interesting thing here is that adding or removing neutrons from an atom does not create a different element. Rather, it creates a heavier or lighter version of that element. These different versions are called isotopes and most elements are actually a mixture of different isotopes.

If you could grab atoms of krypton and count the number of neutrons each one had, you would find that most would have 48, others would have 47, some would have 50, some others would have 46, a few would have 44 and a very few would have 42. You would count different numbers of neutrons because krypton is a mixture of six isotopes.

In Summary...

6 0
3 years ago
PLEASE HELP! DUE DATE IS TODAY
g100num [7]

Answer:

<u>Question 2</u>

<u>Part (a)</u>

Chlorine:  type of compound = chloride

Oxygen:  type of compound = oxide

<u>Part (b)</u>

The iron reacts with water and oxygen to form rust.

A water molecule is made up of two hydrogen atoms joined to one oxygen atom:  Di-hydrogen oxide.

<u>Question 3</u>

This circuit is in parallel.

The current in a parallel circuit splits into different branches then combines again before it goes back into the supply.

We are told that A₁ = 0.8 A

As the lamps have <u>equal resistance</u>, the current splits equally:

A₂ = 0.4 A

A₃ = 0.4 A

Then combines again:

A₄ = 0.8 A

4 0
2 years ago
Prove that g is inversely proportional to the radius​
vaieri [72.5K]

Answer:The acceleration due to gravity g is inversely proportional to the square of the radius in the formula g = GM / R^2 where G is the gravitational constant = 6.67 x 10^-11 Nm^2/kg^2, M is the mass of the Earth and R is the radius of the Earth

Explanation:

4 0
3 years ago
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