Reducing Energy in an RC Capacitor: Solving for Discharge Time

In summary, the problem involves finding the time (in ms) it takes for the energy stored in a capacitor to be reduced to half its initial value, given the value of RC as 7 ms. The equations involved are E=.5CV^2, E=.5Q^2/C, E=.5QV, and Q_f = Q_i * e^(-t/RC). By finding the fraction of the maximum charge (q/2^.5) needed to produce half the energy, the solution can be found by plugging in the values, resulting in an answer of 2.43 ms.
  • #1
hover
343
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Homework Statement


At what time (in ms) after the discharge begins is the energy stored in the capacitor reduced to half its initial value?

RC=7 ms

Homework Equations


RC=7ms
E=.5CV^2
E=.5Q^2/C
E=.5QV
Q_f = Q_i * e^(-t/RC)

The Attempt at a Solution


I don't even know where to go from here. I know that since the problem involves RC, the equation to solve the problem must have some form of Q_f = Q_i * e^(-t/RC) but I'm stuck.
 
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  • #2
hover said:

Homework Statement


At what time (in ms) after the discharge begins is the energy stored in the capacitor reduced to half its initial value?

RC=7 ms

Homework Equations


RC=7ms
E=.5CV^2
E=.5Q^2/C
E=.5QV
Q_f = Q_i * e^(-t/RC)

The Attempt at a Solution


I don't even know where to go from here. I know that since the problem involves RC, the equation to solve the problem must have some form of Q_f = Q_i * e^(-t/RC) but I'm stuck.

Since energy is proportional to the square of charge, by what fraction of the maximum charge should the final charge be to produce half the energy stored with maximum charge?
 
Last edited:
  • #3
xcvxcvvc said:
Since energy is proportional to the square of charge, by what fraction of the maximum charge should the final charge be to produce half the energy stored with maximum charge?

Ah! I see now! When one works the math, the final charge after half the energy is gone is q/2^.5. the initial charge is q. From there it is just plugging into get an the answer 2.43 ms.

Thanks! :D
 

FAQ: Reducing Energy in an RC Capacitor: Solving for Discharge Time

What is an RC capacitor?

An RC capacitor is a type of electrical component that is used to store and release electrical energy in a circuit. It is made up of two conductive plates separated by an insulating material, or dielectric. When a voltage is applied to the capacitor, it stores energy in the form of an electric field between the plates.

How does an RC capacitor store and release energy?

When a voltage is applied to an RC capacitor, it charges up and stores energy in the form of an electric field. As the capacitor discharges, the stored energy is released back into the circuit. The rate at which the capacitor charges and discharges depends on its capacitance and the resistance of the circuit.

What is the relationship between capacitance and energy stored in an RC capacitor?

The energy stored in an RC capacitor is directly proportional to its capacitance. This means that as the capacitance increases, so does the amount of energy that can be stored in the capacitor. This relationship is described by the equation E=1/2CV^2, where E is the energy stored, C is the capacitance, and V is the voltage applied to the capacitor.

Can an RC capacitor store unlimited amounts of energy?

No, an RC capacitor has a maximum energy storage capacity that is limited by its physical size and the dielectric material used. If the capacitor is overcharged, it can become damaged or even explode. It is important to use capacitors with the correct capacitance and voltage ratings for a given circuit to prevent this from happening.

How is an RC capacitor different from other types of capacitors?

An RC capacitor is different from other types of capacitors, such as electrolytic or ceramic capacitors, in that it uses a combination of a resistor and a capacitor to store and release energy. This allows for a more controlled and gradual release of energy compared to other types of capacitors. RC capacitors are also commonly used in timing circuits and filtering applications due to their ability to store energy and release it at a specific rate.

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