Calculating Capacitor Charge & Voltage: A Problem

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Discussion Overview

The discussion revolves around a homework problem involving the calculation of charge, voltage, and energy stored in a capacitor subjected to a specific current over time. The problem includes determining these values at given time intervals and understanding the underlying principles of capacitor behavior in response to current.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that the total charge at time t can be found by integrating the current over time, specifically mentioning the area under the current curve to find the charge at t = 30 µs.
  • Another participant indicates that finding the voltage involves a similar process to that of finding the charge, emphasizing the relationship between charge and voltage through the capacitor's capacitance.
  • A different interpretation is provided regarding the energy stored in the capacitor, suggesting it should be calculated based on the final voltage after charging.
  • A participant expresses gratitude for the assistance received, indicating that the explanations helped clarify their understanding of the problem.

Areas of Agreement / Disagreement

Participants generally agree on the methods for calculating charge and voltage through integration of current, but there is no explicit consensus on the interpretation of the energy calculation, as it is framed differently by one participant.

Contextual Notes

The discussion does not address specific assumptions or limitations regarding the current waveform or the capacitor's characteristics, which may affect the calculations.

Who May Find This Useful

Students working on capacitor-related problems in electrical engineering or physics, particularly those dealing with charge, voltage, and energy calculations in circuits.

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Homework Statement


The current shown below is applied to a 0.25uF capacitor. The initial voltage on the capacitor is zero.
(a) Find the charge on the capacitor at t = 30us.
(b) Find the voltage on the capacitor at t = 50us.
(c) How much energy is stored in the capacitor by this current?

http://img296.imageshack.us/img296/1800/currentgraphyk8.png

http://img513.imageshack.us/img513/302/problemdescriptionqw0.png

Thank you very much for any help you offer. This has had me bogged down for a couple hours now and I just want to understand how they got those answers in the back of the book.
 

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There is no need to "work backwards."

The total charge accumulated at time t is the integral of the current up to time t. So find the area underneath the curve up to t = 30 us in order to find q(30 us). You should get 1.25 uC.
 


Finding the voltage requires exactly the same procedure as I described above for the charge. (After all, the voltage is simply proporational to the charge accumulated). You can see that from the equation you've been given. You just have to compute the integral up until t = 50 us, and then divide the answer by C.
 


I interpret part c to be asking how much energy is stored in the process of charging up this capacitor using this current (i.e., at the end of it all, how much energy is stored)? Therefore, all you have to do is calculate the energy based on the capacitor's final voltage.
 


Thank you very much for your help. It all works out now.
 

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