How many time constants must elapse in a capacitor?

AI Thread Summary
To determine how many time constants must elapse for a capacitor to discharge 55% of its stored energy, one must consider the equations governing RC circuits. The energy stored in a capacitor is given by the formula U = 1/2 CV^2, where C is capacitance and V is voltage. The voltage across the capacitor during discharge decreases exponentially over time, described by V(t) = V0 e^(-t/RC). To find the time constant needed for a 55% energy loss, the relationship between energy and voltage must be analyzed, leading to the conclusion that a specific number of time constants can be calculated based on these equations. Understanding these principles is essential for solving the problem effectively.
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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