When two capacitors are connected in parallel and then connected to a battery, the total stored energy is 6.7 times greater than when they are connected in series and then connected to the same battery. what is the ratio of the two capacitances?

4.48 and 0.22

Explanation:

Below are the stated formulas for capacitors in series and parallel.

Let both capacitors be C1 and C2 respectively.

For parallel:

Total C = C1 + C2

For series (after rearranging the formular):

Total C = C1C2 / (C1 + C2)

Now, formular to calculate total  energy stored is given below.

Parallel:

E = 1/2 * CV^2

 = 1/2 * (C1 + C2) * V^2

Series:

E = 1/2 * CV^2

= 1/2 * (C1C2/ (C1 + C2)) * V^2

In the question, it states that energy stored in parallel is 6.7 times the energy when stored in series.

E(parallel) = 6.7E(series)

1/2 * (C1 + C2) * V^2 = 6.7 * 1/2 * (C1C2/ (C1 + C2)) * V^2

(C1 + C2) = 6.7C1C2 / (C1 + C2)     (cancelling out V^2 and 1/2 on both sides)

(C1 + C2)^2 = 6.7C1C2

C1^2 + 2C1C2 + C2^2 = 6.7C1C2

C1^2 - 4.7C1C2 + C2^2 = 0

Now,we need to divide through by C2^2 to get an equation of the form ax^2 + bx + c = 0, which we can then solve using the quadratic equation.

C1^2 / C2^2 - 4.7C1 / C2 + 1 = 0

let x = C1 / C2     (x is the ratio of the capacitance of the capacitors)

x^2 - 4 x + 1 = 0

Using the quadratic equation, the solutions are:

x = C1 / C2 = 4.48 and x = C1 / C2 = 0.22 in two decimal places.

quantum mechanics or quantum physics is physics of very small objects (particles) and physical entities.

quantum physics has some parallels to our macro world and some pretty unique ideas which theoretically and mathematically proven to be true even though we will never be able to access them because of our size.

there are many types of particles: subatomic, elementary etc.

subatomic means they are smaller than atom, elementary means they are at the very basis of everything.

subatomic particles are for eg. protons, neutrons but not electrons.

elementary particles are categorised into 3 groups by what they do.

these 3 groups are quarks, leptons and bosons.

light for example is a particle more precisely a photon a part of leptons.

proton (subatomic particle) is made out of 2 up quarks and 1 down quark each of these has a fractional charge like . (i crazy)

most famous scientist who contributed to this physics are:

the topic itself us understand a lot and will probably be vastly used in the future (quantum computers, understanding the big bang,

we also must not forget quantum effects like:

and there is more. but probably too much for this answer to be consistent due to my average understanding of this topic.

hope this you understand quantum mechanics a little more. i'm not an expert in the topic (so don't be like wth if you are an expert) but i'm very interested in it.

anyways quantum physics is a very hard topic (harder than physics (perhaps)) therefore searching for every information there is about it and learning it is unfortunately impossible (you can only specialise into 1 - 3 things or more (perhaps

have fun and i wish you luck!

r3t40