TeXercises.com

Maximising Energy

About points...

We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.

That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.

About difficulty...

We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.

That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:

Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise

Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise

Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise

Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise

Level 5 -
Level 6 -

Exercise

Physics Electricity Electrostatics

https://texercises.raemilab.ch/exercise/maximising-energy/

Question

Solution

Short

Video

\(\LaTeX\)

No explanation / solution video to this exercise has yet been created.

Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!

Exercise:
If your goal is to make a parallel plate capacitor with the highest possible energy storage capacity is it better to aim for a small or a large distance between the plates?

Solution:
The energy stored in a capacitor is given by sscWE frac C Delta V^ The capacitance is inversely proportional to the distance between the plates: C varpropto fracd For a given dielectric there is a certain maximum electric field strength em dielectric strength sscEmax before it breaks down. The em breakdown voltage is therefore sscDelta Vmax sscEmax d varpropto d i.e. for the same electric field strength the voltage between the plates is proportional to the plates' distance. For the overall depency of the energy on the distance between the plates we thus find sscWE &varpropto fracd d^ d With respect to a large amount of energy stored in the capacitor it is therefore better to aim for a large plate distance but of course this is contrary to the goal of having a high energy em density.

Report An Error

Description: Reporter: Email:

You are on texercises.raemilab.ch.
reCaptcha will only work on our main-domain \(\TeX\)ercises.com!

Meta Information

\(\LaTeX\)-Code

Contained in these collections:

Capacitors (Advanced) by by

9 | 10

Attributes & Decorations

Branches	Electrostatics
Tags	capacitor, electric potential energy, parallel plate capacitor
Content image
Difficulty	(1, default)
Points	0 (default)
Language	(English)
Type	Calculative / Quantity
Creator	by
Decoration