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Capacitance
19 questions By Tony R. Kuphaldt
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Question 16 of 19
∫f(x) dx Calculus alert!
Ohm’s Law tells us that the amount of current through a fixed resistance may be calculated as such:I = E RWe could also express this relationship in terms of conductance rather than resistance, knowing that G = 1/R:
I = EG However, the relationship between current and voltage for a fixed capacitance is quite different. The “Ohm’s Law” formula for a capacitor is as such:
i = C de dtWhat significance is there in the use of lower-case variables for current (i) and voltage (e)? Also, what does the expression de/dt mean? Note: in case you think that the d’s are variables, and should cancel out in this fraction, think again: this is no ordinary quotient! The d letters represent a calculus concept known as a differential, and a quotient of two d terms is called a derivative.
Reveal answerLower-case variables represent instantaneous values, as opposed to average values. The expression de/dt, which may also be written as dv/dt, represents the instantaneous rate of change of voltage over time.
Follow-up question: manipulate this equation to solve for the other two variables de/dt = … ; C = …).
Notes:I have found that the topics of capacitance and inductance are excellent contexts in which to introduce fundamental principles of calculus to students. The time you spend discussing this question and questions like it will vary according to your students’ mathematical abilities.
Even if your students are not ready to explore calculus, it is still a good idea to discuss how the relationship between current and voltage for a capacitance involves time. This is a radical departure from the time-independent nature of resistors, and of Ohm’s Law!
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Question 17 of 19
Complete this statement by substituting the correct electrical variables (voltage, current, resistance, capacitance):
- Capacitors oppose changes in (fill-in-the-blank), reacting to such changes by producing a (fill-in-the-blank).
Reveal answerCapacitors oppose changes in voltage, reacting to such changes by producing a current.
Notes:Emphasize to your students that capacitance is an essentially reactive property, opposing change in voltage over time. It is not steady voltage that capacitors react to, only changing voltage.
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Question 18 of 19
Electrical capacitance has a close mechanical analogy: elasticity. Explain what the term “elasticity” means for a mechanical spring, and how the quantities of velocity and force applied to a spring are respectively analogous to current and voltage applied to a capacitance.
Reveal answerAs a spring is compressed at a constant velocity, the amount of reaction force it generates increases at a linear rate:
v = 1 kdF dtWhere,
v = Velocity of spring compression
k = Spring “stiffness” constant
F = Reaction force generated by the spring’s compression
t = Time
In a similar manner, a pure capacitance experiencing a constant current will exhibit a constant rate of voltage change over time:
i = C de dtNotes:Note to your students that spring stiffness (k) and capacitance (C) are inversely proportional to one another in this analogy.
Explain to your students how the similarities between inertia and capacitance are so close, that capacitors can be used to electrically model mechanical springs!
