Confused on the power through a Capacitor formula help

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SUMMARY

The discussion centers on understanding the power through a capacitor and its relationship to energy storage, specifically using the formula U = 1/2 CV². The user is confused about deriving power from energy, particularly when energy is treated as a constant. The correct approach involves recognizing that power is the derivative of energy with respect to time, and that the voltage across a capacitor can be expressed as a function of time, typically involving an exponential decay related to the circuit's time constant.

PREREQUISITES
  • Understanding of capacitor fundamentals, including capacitance (C) and charge (Q).
  • Knowledge of the energy stored in capacitors, specifically U = 1/2 CV².
  • Familiarity with calculus, particularly derivatives and their application in physics.
  • Basic circuit theory, including the role of switches and time constants in RC circuits.
NEXT STEPS
  • Study the derivation of power in capacitors using calculus.
  • Learn about exponential functions in the context of RC circuits and their time constants.
  • Explore the relationship between charge (Q), voltage (V), and capacitance (C) in dynamic circuits.
  • Investigate practical applications of capacitors in electronic circuits, focusing on energy storage and discharge behavior.
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Students and professionals in electrical engineering, physics enthusiasts, and anyone seeking to deepen their understanding of capacitor behavior in circuits.

nchin
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I know that the energy stored in a capacitor is U = 1/2 CV2. but the power through it? I have in my notes that the power is the derivative of U.

so for example the energy is 26 Joules so the derivative of 26 J? doesn't make sense cause 26 is a constant.

help please!

i attached a picture of the problem. i first find the C equivalent.

oops! there's actually a switch on the top of the circuit! which closes at t = 0
 

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Can you find an expression for the potential across the equivalent capacitance with respect to time? How about the stored energy? This expression should be differentiable w.r.t. time...
 
gneill said:
Can you find an expression for the potential across the equivalent capacitance with respect to time? How about the stored energy? This expression should be differentiable w.r.t. time...

potential across is C = QV --> V(t) = C/Q(t). is that it?
 
nchin said:
potential across is C = QV --> V(t) = C/Q(t). is that it?

No. C is capacitance, not potential. C = QV is not a correct formula. And Q(t) does not provide any information about how the charge Q changes over time.

What is the expression for the voltage across the capacitance with respect to time for the given circuit? Hint: it involves an exponential function with a time constant.
 
Last edited:

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