How many time constants must elapse in a capacitor?

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SUMMARY

The discussion centers on calculating the time constants required for a capacitor to discharge 55% of its stored energy through a resistor in an RC circuit. The relevant equations include the energy stored in a capacitor, given by the formula \(E = \frac{1}{2}CV^2\), and the discharge behavior characterized by the time constant \(τ = RC\). To determine the number of time constants needed for a 55% energy discharge, one must apply the exponential decay formula related to capacitor discharge.

PREREQUISITES
  • Understanding of RC circuits and time constants
  • Familiarity with the energy storage formula for capacitors
  • Knowledge of exponential decay functions
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of the capacitor discharge formula in RC circuits
  • Learn how to calculate energy stored in capacitors using \(E = \frac{1}{2}CV^2\)
  • Explore the concept of time constants in electrical circuits
  • Investigate practical applications of capacitors in electronic devices
USEFUL FOR

Students in electrical engineering, physics enthusiasts, and anyone seeking to understand capacitor behavior in circuits will benefit from this discussion.

yogotah
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Homework Statement



How many time constants must elapse if an initially charged capacitor is to discharge 55% of its stored energy through a resistor?

Homework Equations





The Attempt at a Solution


I don't even know where to start, so please a nudge in the right direction would help.

Thanks!
 
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yogotah said:

Homework Statement



How many time constants must elapse if an initially charged capacitor is to discharge 55% of its stored energy through a resistor?

Homework Equations





The Attempt at a Solution


I don't even know where to start, so please a nudge in the right direction would help.

Thanks!

Well, what equations do you know that might be related to the problem? Clearly there's an RC circuit with the capacitor discharging from some initial value (charge or voltage, either will do). What's the expression that describes that? What's an expression for the energy stored in a capacitor?
 

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