Facebook
Google
GitHub
LinkedinDC Electric Circuits
Time Constant Calculations
52 questions By Tony R. Kuphaldt
-
Question 4 of 52
At a party, you happen to notice a mathematician taking notes while looking over the food table where several pizzas are set. Walking up to her, you ask what she is doing. Ï‘m mathematically modeling the consumption of pizza,” she tells you. Before you have the chance to ask another question, she sets her notepad down on the table and excuses herself to go use the bathroom.
Looking at the notepad, you see the following equation:
Percentage = (e−[t/6.1]) ×100% Where,
t = Time in minutes since arrival of pizza.
The problem is, you don’t know whether the equation she wrote describes the percentage of pizza eaten or the percentage of pizza remaining on the table. Explain how you would determine which percentage this equation describes. How, exactly, can you tell if this equation describes the amount of pizza already eaten or the amount of pizza that remains to be eaten?
Reveal answerThis equation models the percentage of pizza remaining on the table at time t, not how much has already been eaten.
Notes:While some may wonder what this question has to do with electronics, it is an exercise in qualitative analysis. This skill is very important for students to master if they are to be able to distinguish between the equations e−[t/(τ)] and 1 − e−[t/(τ)], both used in time-constant circuit analysis.
The actual procedure for determining the nature of the equation is simple: consider what happens as t begins at 0 and as it increases to some arbitrary positive value. Some students may rely on their calculators, performing actual calculations to see whether the percentage increases or decreases with increasing t. Encourage them to analyze the equation qualitatively rather than quantitatively, though. They should be able to tell which way the percentage changes with time without having to consider a single numerical value!
-
Question 5 of 52
The following two expressions are frequently used to calculate values of changing variables (voltage and current) in RC and LR timing circuits:
e−[t/(τ)] or 1 − e−[t/(τ)] One of these expressions describes the percentage that a changing value in an RC or LR circuit has gone from the starting time. The other expression describes how far that same variable has left to go before it reaches its ultimate value (at t = ∞).
The question is, which expression represents which quantity? This is often a point of confusion, because students have a tendency to try to correlate these expressions to the quantities by rote memorization. Does the expression e−[t/(τ)] represent the amount a variable has changed, or how far it has left to go until it stabilizes? What about the other expression 1 − e−[t/(τ)]? More importantly, how can we figure this out so we don’t have to rely on memory?
Reveal answerHere is a hint: set x to zero and evaluate each equation.
Notes:It is very important for students to understand what this expression means and how it works, lest they rely solely on memorization to use it in their calculations. As I always tell my students, rote memorization will fail you! If a student does not comprehend why the expression works as it does, they will be helpless to retain it as an effective “tool” for performing calculations in the future.
-
Question 6 of 52
Graph both the capacitor voltage (VC) and the capacitor current (IC) over time as the switch is closed in this circuit. Assume the capacitor begins in a complete uncharged state (0 volts):
Then, select and modify the appropriate form of equation (from below) to describe each plot:
e−[t/(τ)] 1 − e−[t/(τ)] Reveal answer
IC = Imax (e−[t/(τ)]) VC = Vmax (1 − e−[t/(τ)]) Notes:Have your students explain why the voltage and current curves are shaped as they are.
Maybe this will help someone else. The general formulas for V(t) and I(t) in question 25 (and the x(t) versions in question s 23 and 14) contain typos (or maybe hypertext coding glitches). They should actually be V(t) = (Vf-Vo)(1-e^(-t/𝛕)) + Vo, I(t) = (If-Io)(1-e^(-t/𝛕)) + Io in question 25. Those are correct in the PDF download version. In questions 23 and 24 the equations are x = xinitial + ( xfinal − xinitial ) ( 1 − e[(−t)/(τ)] ).