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Capacitors
15 questions By Tony R. Kuphaldt
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Question 7 of 15
A 470 μF capacitor is subjected to an applied voltage that changes at a rate of 200 volts per second. How much current will there be “through” this capacitor?
Explain why I placed quotation marks around the word “through” in the previous sentence. Why can’t this word be used in its fullest sense when describing electric current in a capacitor circuit?
Reveal answerThis capacitor will have a constant current of 94 milliamps (mA) going “through” it. The word “through” is placed in quotation marks because capacitors have no continuity.
Notes:Don’t give your students the equation with which to perform this calculation! Let them find it on their own. The [dv/dt] notation may be foreign to students lacking a strong mathematical background, but don’t let this be an obstacle to learning! Rather, use this as a way to introduce those students to the concept of rates of change, and to the calculus concept of the derivative.
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Question 8 of 15
Two 470 μF capacitors connected in series are subjected to a total applied voltage that changes at a rate of 200 volts per second. How much current will there be “through” these capacitors? Hint: the total voltage is divided evenly between the two capacitors.
Now suppose that two 470 μF capacitors connected in parallel are subjected to the same total applied voltage (changing at a rate of 200 volts per second). How much total current will there be “through” these capacitors?
Reveal answerSeries connection: 47 milliamps (mA) total. Parallel connection: 188 milliamps (mA) total.
Follow-up question: what do these figures indicate about the nature of series-connected and parallel connected capacitors? In other words, what single capacitor value is equivalent to two series-connected 470 μF capacitors, and what single capacitor value is equivalent to two parallel-connected 470 μF capacitors?
Notes:If your students are having difficulty answering the follow-up question in the Answer, ask them to compare these current figures (47 mA and 188 mA) against the current that would go through just one of the 470 μF capacitors under the same condition (an applied voltage changing at a rate of 200 volts per second).
It is, of course, important that students know how series-connected and parallel connected capacitors behave. However, this is typically a process of rote memorization for students rather than true understanding. With this question, the goal is to have students come to a realization of capacitor connections based on their understanding of series and parallel voltages and currents.
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Question 9 of 15
Suppose two 33 μF capacitors are connected in series with each other. What will their combined capacitance be, in Farads? Explain your answer.
Reveal answer16.5 μF
Notes:Capacitors often confuse new students of electronics because their values do not add up the same as resistors. It is important in answering this question that your students understand why series capacitances combine as they do. There is more than one way to explain this phenomenon - explain in terms of capacitor dimensions, or in terms of voltage drop and charge storage.
