Initially charged capacitor disharged through a resistor

In summary, the time required for a capacitor with initial charge q0 to lose one-third of its charge is equal to RC*ln(3) where RC is the time constant. The same applies for losing two-thirds of its charge.
  • #1
Mike88
6
0

Homework Statement


A capacitor with initial charge q0 is discharged through a resistor.
(a) In terms of the time constant τ, how long is required for the capacitor to lose the first one-third of its charge? answer x tau
(b) How long is required for the capacitor to lose the first two-thirds of its charge?
answer x tau



Homework Equations


i = -(q0/RC)e(-t/RC)


The Attempt at a Solution


I tried solving for time t and got -RC*ln(q/q0)= t
I'm lost i don't know what to do
 
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  • #2
Mike88 said:
I tried solving for time t and got -RC*ln(q/q0)= t
Looks good to me (except for the minus sign). So what's the time when q = q0/3?
 
  • #3
Doc Al said:
Looks good to me (except for the minus sign). So what's the time when q = q0/3?

i then get t = RC*ln(1/3) where RC = tau

is this correct?
 
Last edited:
  • #4
Mike88 said:
i then get t = RC*ln(1/3) where RC = tau

is this correct?
Yes. But put that minus sign back in. (I didn't see that you had q0 on top! :wink:)
 
  • #5
Doc Al said:
Yes. But put that minus sign back in. (I didn't see that you had q0 on top! :wink:)

thanks for the help i figured out everything.
 

FAQ: Initially charged capacitor disharged through a resistor

What is an initially charged capacitor?

An initially charged capacitor is a device that stores electrical energy in the form of an electric charge. It consists of two conductive plates separated by a dielectric material, usually air or a non-conductive material. When connected to a power source, one plate accumulates a positive charge while the other accumulates a negative charge, creating an electric field between them.

How does a capacitor discharge through a resistor?

When a capacitor is connected to a resistor, the electric charge stored on its plates begins to flow through the resistor. This flow of charge is known as current. As the capacitor discharges, the voltage across it decreases, and the current eventually stops when the capacitor becomes fully discharged.

What is the time constant of a discharging capacitor?

The time constant of a discharging capacitor is a measure of how quickly it discharges through a resistor. It is calculated by multiplying the resistance of the circuit by the capacitance of the capacitor. The time constant determines the rate at which the capacitor discharges, with a higher time constant leading to a slower discharge.

What happens to the energy stored in a capacitor when it discharges through a resistor?

As the capacitor discharges through a resistor, the energy stored in it is converted into heat. This is because the resistor dissipates the energy as it opposes the flow of current. The amount of energy dissipated is equal to the product of the voltage across the resistor and the current flowing through it.

Why is a resistor necessary in discharging a capacitor?

A resistor is necessary in discharging a capacitor because it limits the flow of current through the circuit. Without a resistor, the capacitor would discharge too quickly, potentially causing damage to the circuit. The resistor also ensures that the capacitor discharges in a controlled manner, making it safer to handle.

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