5.E (all of 5.4-5.6) Capacitor Maths Flashcards
Exponential Decay Exponential Growth Graphs (logs) Time Constant Graphical Determination
What is exponential growth?
When something gets larger by the same fraction or proportion in the same amount of time.
What is exponential decay?
When something gets smaller by the same fraction or proportion in the same amount of time.
How to show values are decresing/increasing exponentially?
Take consecutive values and divide first by second (keep going with 2nd and 3rd, then 3rd and 4th…..etc). If the roughly the same ratio is kept throughout all of them then it is exponential.
What is a log line graph?
A graph with logarithmic y axis and linear x axis.
What does this graph show and what does it hide?
It usually shows a straight line, however the exponential function can still apply
What is special about this straight line?
It doesn’t go through the origin.
When a capacitor discharges, what is the relationship between time and charge/current/pd and time.
as time increases the current/pd/charge decreases by 1/e^t
What a capacitor charges, what is the relationship between charge/pd and time?
as time increases the charge/pd increase by 1-1/e^t
Why doesn’t this apply to current?
Current always decreases.
Why do we often choose to create log-lin graphs? What would usually be the time constant?
Easier to find the time constant.
The gradient
What kind of curve is created with an exponential graph?
concave
GGreater resistance means what for the time constant?
It becomes greater as capacitor will take longer to discharge
How would I find the time constant of a q/t graph showing fully charged capacitor?
Max charge x 1/e to find charge at which value falls exponentially. Read off time
How would I find the time constant of a pd/t graph showing fully charged capacitor?
Max pd x 1/e to find charge at which value falls exponentially. Read off time
