Time constant question in an AQA exam paper

[bonbon22]

Homework Statement

Determine the number of different readings the student will be able to take before the
capacitor becomes fully charged.
https://filestore.aqa.org.uk/resources/physics/AQA-74083A-SQP.PDF
question 2.5
image below

Relevant Equations

Time constant = resistance * capatiance

I assumed that i had to take 5 time constants which would give the time taken to charge fully i assume then divide by 10 giving me a total number of readings of 34 ,
the answer is 6
yet they only used a single time constant to determine the number of readings? as this give me an answer of 68 or 6.8 readings therefore 6

 

[TSny]

The concept of "time constant" is not very relevant to this problem since the resistance is continually varied during the charging process.

Some things you might want to consider:

(1) What is the final charge on the capacitor?

(2) In order for the current to remain constant, does the resistance need to be increased or decreased during the charging process?

I wasn't sure of the wording of the problem. It says, "The variable resistor has a maximum value of 100 kΩ". I guess that this means that during the charging process, the maximum value of the resistance of the resistor is 100 kΩ.

 

[DaveE]

I find the following part of the question most interesting "... a suitable ammeter reading".
Another poorly worded homework question (sigh). Suppose you initially adjust the resistance to zero, then there are zero readings taken (or maybe 1, I'm not sure how fast they think you are, LOL). So, you are forced to make an assumption about the initial state. I like TSny's version, the resistor maximum is 100Kohm, because any other value seems completely arbitrary. Would it really be so hard to clearly and explicitly state the initial conditions when asking a question about how a circuit responds?
Why I hate these computerized tests: They force you to input a number when an equation is the only good answer. (ie. number of measurement vs, initial current setting). So you have to guess how the question should have been written.

 

[SammyS]

One could (weakly) argue that when the question is asked as to determine "the number of different reading the student be able to take", the intended meaning is to find the maximum number of readings possible, before the capacitor is fully charged to 6V .

Of course, that requires starting with the maximum resistance available.

 

[CWatters]

Do they expect you to know equations like

Q=VC
and so
I=CdV/dt

For this paper?

If so then rearrange I=CdV/dt to give

dt=CdV/I.....(1)

Then you have to assume the current I starts and stays at 6V/100kOhms. If you substitute values into equation 1 you find things cancel and give dt=68seconds or 6.8 sample periods.

Aside: Feeding a constant current into a capacitor is a standard way to generate a triangle wave.

 

[bonbon22]

cheers everyone i get it now, current is constant as the question stated and its a variable resistor so i can't use the time constant equation. 5RC doesn't work here . So i would have went for some other method.

 

[CWatters]

I note this isn't just a badly worded homework question. This is a badly worded exam question that could determine if your/my child gets into university. I'm shocked.

 

[bonbon22]

I note this isn't just a badly worded homework question. This is a badly worded exam question that could determine if your/my child gets into university. I'm shocked.

this is a specimen paper so its not an actual paper aqa give out to students. Speciman papers have a reputation for having mistakes or werid questions for any exam borad as the question making go through a smaller team of people. I wouldn't worry too much about that most of the papers are pretty fair tbh. If your child works harder than every other student since grade boundaries determine grades then they'll get into university

 

[CWatters]

I thought about this question more overnight. If the marking scheme gives full marks for any reasonable value of R, I and the corresponding number of samples then it's not an unreasonable question.

For example setting R to 60k giving I=0.1mA and 40.8s or 4 samples should also be a valid answer as it doesn't ask for the maximum number of possible samples.

 

[bonbon22]

I thought about this question more overnight. If the marking scheme gives full marks for any reasonable value of R, I and the corresponding number of samples then it's not an unreasonable question.

For example setting R to 60k giving I=0.1mA and 40.8s or 4 samples should also be a valid answer as it doesn't ask for the maximum number of possible samples.

the answer was 6