How much energy in microjoules is stored in the capacitor

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Discussion Overview

The discussion revolves around calculating the energy stored in a capacitor at specific time intervals, particularly at 500 microseconds and as time approaches infinity. Participants explore various approaches to the problem, including the use of graphs and mathematical equations related to current, charge, and voltage.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses uncertainty about how to approach the problem, questioning whether the tangent line to the current versus time graph represents energy.
  • Another participant clarifies that the tangent represents the rate of change of current, not energy, and prompts others to recall formulas for energy stored in a capacitor.
  • Several participants mention the formula for energy stored in a capacitor, noting the relationship between capacitance, voltage, and charge.
  • One participant attempts to calculate charge using integration of a given function but reports not obtaining the correct answer.
  • Another participant points out a misunderstanding regarding the units of electrical quantities, emphasizing that energy is measured in Joules, not in milliamperes.
  • There are repeated inquiries about the significance of the area under the curve in relation to current and charge, suggesting that integrating current over time yields total charge.
  • One participant eventually reports success in calculating voltage and energy using a specific method involving integration and the energy formula.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct approach to the problem, as there are multiple attempts and methods discussed, with some participants expressing confusion and others providing corrections or alternative perspectives.

Contextual Notes

There are limitations in the discussion regarding the clarity of the formulas used and the assumptions made about the relationships between current, charge, and voltage. Some participants struggle with unit conversions and the implications of their calculations.

ME_student
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Homework Statement


a) How much energy in microjoules is stored in the capacitor at t=500 micro sec
b) Repeat (a) for t=infinite

Homework Equations


Will be on attachment

The Attempt at a Solution


I am not sure how to approach the problem.. The graph shown is a graph of amps respect to time. So the tangent line to the function curve is joules?
 

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The tangent to a current versus time curve would be ΔI/Δt, or di/dt. That's not energy.

What's a formula for the energy stored on a capacitor? You should know one in terms of voltage and another in terms of charge (Coulombs). How might you find the total charge or voltage on the capacitor from the given curve? Note that you also have the formula for the curve, so you can work the problem symbolically.
 
Energy stored on a capacitor is given by C=(epsilon*A)/(d)

Epsilon is a constat
A is the area of the plate
d is the distance between the plates

the equation with voltage is Q=C*dv/dt
 
I am currently working on the problem. I am trying to understand what the tangent to the graph or the total area underneath a graph represents when you have a graph that may have voltage respect to resistance, power respect to resistance, current respect to time, etc.
 
I said Q=integral of 50e^-2000t with limits of integration of 0 to 500microsec. I get 0.015803mA then I used C=Q/v to get volate. After that I use w=1/2(CV^2)

But I don't get the correct answer.
 
Last edited:
ME_student said:
Energy stored on a capacitor is given by C=(epsilon*A)/(d)

Epsilon is a constat
A is the area of the plate
d is the distance between the plates
You seem to be having some difficulty distinguishing the units of various electrical quantities. The above formula yields C, the Capacitance of the capacitor, not the energy. Energy has the units Joules.
the equation with voltage is Q=C*dv/dt
And that's an expression for the current (I in amps) , or rate of change of change charge (Coulombs) on the capacitor.
 
ME_student said:
I am currently working on the problem. I am trying to understand what the tangent to the graph or the total area underneath a graph represents when you have a graph that may have voltage respect to resistance, power respect to resistance, current respect to time, etc.
If you integrate current over time what do you get? Remember that current is the rate of flow of charge, or dQ/dt. That means the area under the curve represents...?
 
ME_student said:
I said Q=integral of 50e^-2000t with limits of integration of 0 to 500microsec. I get 0.015803mA then I used C=Q/v to get volate. After that I use w=1/2(CV^2)

But I don't get the correct answer.
Okay, that method is correct, but your value for charge Q is not correct and the units will not be current (mA) but Coulombs (C). Can you show more detail for your integration steps?
 
I got it figured out... I used V(t)=1/C integral i dT+V(0) I got 11.06v and then used w=1/2*CV^2 to find energy
 

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