Question
(a) Calculate the capacitance needed to get an $RC$ time constant of $1.00 \times 10^3 \textrm{ s}$ with a $0.100 \Omega$ resistor. (b) What
is unreasonable about this result? (c) Which assumptions are responsible?
Final Answer
- $10.0 \textrm{ kF}$
- Such a large capacitor would be unrealistically large.
- It isn't reasonable to expect such a large time constant with such a small resistor.
Solution Video
OpenStax College Physics Solution, Chapter 21, Problem 77 (Problems & Exercises) (0:39)
Sign up to view this solution video!
View sample solutionCalculator Screenshots
Video Transcript
This is College Physics Answers with Shaun Dychko.
We're identifying the capacitance needed to get a time constant of one times ten to the three seconds with a 0.1 Ohm resistor. And the time constant is resistance times capacitance so divide both sides by R and we get C as tau over R. So that's one times ten to the three seconds divided by 0.1 Ohms which is 10 Kilo Farads or ten times to the three Farads. And such a large capacitor is unrealistically large and would not be reasonable to expect such a large time constant of ten to the three seconds given such a small resistance of only 0.1 Ohms.