Is there a must to have a fixed capacitor and various resistors in a circuit to obtain different time constant?

Is it better to have a higher resistor value or capacitor value? Why?

 

It depends upon the impedance of the circuit containing the resistor and capacitor. Normally you use as high a value of resistor as the circuit loading allows (for example the input impedance and bias current of an op amp). This makes the capacitor physically smaller for a given time-constant and perhaps avoids the use of electrolytics which have poor stability and relatively high leakage.

 

What if in a DC circuit,
time constant can be obtained by 2 options

a) 56kΩ x 1000µF = 56 seconds
b) 28kΩ x 2000µF = 56 seconds

which one is better?

 

What if in a DC circuit,
time constant can be obtained by 2 options

a) 56kΩ x 1000µF = 56 seconds
b) 28kΩ x 2000µF = 56 seconds

which one is better?

Depends on what your metric for "better" is.

Which is better, a Chevrolet Corvette or a Ford F-250? If the metric is "which one will corner better on the highway?" you will get a much different answer than if the metric is "which one will would I rather mount a snow plow on the bumper?"

This is a recurring problem in engineering (and not just with engineering students, either). We are asked to find the "best" or the "optimal" or the "simplest" but not told what the metric for "best", "optimal", or "simple" are.

So it you take some time to think about what metrics might be important, you can probably come up with your own answers. For instance, if your concern is battery life, you want the combination that will draw less charge from the battery during each charge-discharge cycle. But if your concern is thermal or other type of noise, then your answer may be different.

 

What do you know about the relative sizes and costs of the four components - resistors and capacitors?

 

Is it better to have a higher resistor value or capacitor value? Why?

Have you thought about my question?

 

And lot's of other things. What is connected on the other side of things? What is the situation in steady state? Is there something that is drawing current from the capacitor? You gave two options that were a factor of two apart, but what about two other options that are much further apart:

c) 5.6MΩ x 10µF = 56 seconds
d) 28Ω x 2F = 56 seconds

Which one is better?

The only possible answer is... it depends.

Think of it this way. Let's say that someone were to answer your question and say, "Answer B is better." Would that satisfy you? Hopefully not. Hopefully your next question would be, "Why is it better?" But at that point any answer that is given has to be in terms of the metrics by which "better" is determined. For instance, "Because larger capacitors look more impressive." Well, that means that impressive looks is a key component of the metric. But does it really matter that it's "better" in terms of the metrics used by the person answering the question? No. It should be "better" in terms of the metrics of the person asking the question. But to do that, the person asking the question must supply, explicitly or implicitly, the metrics to be used.

 

the metrics to be used.

Actually I think there is more to it than that. Remember this is for a timing circuit and some capacitors require a polarising voltage.

I am simply trying to draw Katherine to think about the question, which may have been homework anyway.

 

Ah, but if it is for an application that can't tolerate a polarized capacitor, then that is part of the metrics that need to be considered.

And by all means, continue drawing!