Capacitor Discharge Time: How Long to Reach 99% Charge?

In summary, we are trying to find the time it takes for a capacitor to reach 99% of its final charge of 5 uC when connected in series with a 10 k ohms resistor and a 6 V battery of negligible internal resistance. Using the equation Q=Qf(1-e^(-t/T)), where t is time and T is the time constant defined by T=RC, we can solve for t and convert it to milliseconds if needed. However, there may be an algebra mistake in the given solution as the desired answer should be 0.898.. and not 0.99.
  • #1
fball558
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0
capacitor discharge?

Homework Statement



A 1.4 uF capacitor, initially uncharged, is connected in series with a 10 k ohms resistor and a 6 V battery of negligible internal resistance.

How long does it take the capacitor to reach 99% of its final charge?

this is part b. i already found out part a which asked What is the charge on the capacitor after a very long time?
answer to this part was 8.4 uC


Homework Equations



for part b i think i will have to use the equation
Q=Qf(1-e^(-t/T)) where t is time and T is the time constant defined by T= RC



The Attempt at a Solution



i plugged in arbatrary values just to define my 99% i picked 5 but that should not matter

5=4.95(1-e^(-t/(10000*1.4e-6)))
solve for t
this will be in seconds i assume and my answer wants it displayed in ms
i got an answer of around 32 ms but it says I am wrong.
any help would be great!
 
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  • #2


fball558 said:

The Attempt at a Solution



i plugged in arbatrary values just to define my 99% i picked 5 but that should not matter

5=4.95(1-e^(-t/(10000*1.4e-6)))
solve for t
this will be in seconds i assume and my answer wants it displayed in ms
i got an answer of around 32 ms but it says I am wrong.
any help would be great!

First of all, the 5 and 4.95 should be switched around. If 5 is the final charge Qf, then you want to know when Q=4.95. Other than that, your equation is correct.

I get 1 - e^(-0.032/0.014) = 0.898.., not 0.99 as desired. So you probably made an algebra mistake somewhere in getting the 0.032 sec answer.
 
  • #3


I would first validate the equation being used to solve for the discharge time of the capacitor. The equation Q=Qf(1-e^(-t/T)) is a valid equation for calculating the charge on a capacitor at a given time, but it may not be the most appropriate equation for this specific scenario. It is important to consider the assumptions and limitations of this equation, such as assuming a constant voltage and neglecting any other factors that may affect the discharge time.

In order to accurately calculate the discharge time of this specific capacitor, we would need to consider the capacitance, resistance, and voltage values, as well as any other factors that may affect the discharge. Additionally, it may be helpful to use a simulation or experimental setup to confirm the calculated value.

Once the equation and values have been validated, I would suggest double-checking the calculations to ensure accuracy. If the calculated value is still incorrect, it may be helpful to seek guidance from a peer or instructor to troubleshoot the issue. It is also important to clearly state the units in the final answer, in this case, milliseconds.

Overall, as a scientist, it is important to approach problems with a critical and analytical mindset and to validate all assumptions and calculations to ensure accurate results.
 

1. How does the capacitor discharge time affect the performance of a circuit?

The capacitor discharge time is an important factor in determining the overall performance of a circuit. A shorter discharge time allows for faster, more efficient operation of the circuit, while a longer discharge time can slow down the circuit and potentially cause malfunctions.

2. What factors influence the discharge time of a capacitor?

The discharge time of a capacitor is affected by several factors, including the capacitance of the capacitor, the resistance in the circuit, and the initial charge of the capacitor. Higher capacitance and lower resistance will result in a longer discharge time, while a higher initial charge will result in a shorter discharge time.

3. Can the discharge time of a capacitor be calculated?

Yes, the discharge time of a capacitor can be calculated using the formula t = RC, where t is the discharge time in seconds, R is the resistance in ohms, and C is the capacitance in farads. This formula assumes a simple RC circuit with no other components.

4. How long does it take for a capacitor to reach 99% charge?

The time it takes for a capacitor to reach 99% charge (also known as the time constant) is equal to 5 times the discharge time. So, if the discharge time is calculated to be 1 second, the time constant would be 5 seconds.

5. Why is it important to reach 99% charge in a capacitor?

Reaching 99% charge in a capacitor is important because it allows for maximum utilization of the stored energy. The remaining 1% charge is typically negligible and does not significantly affect the performance of the circuit. Additionally, reaching 99% charge ensures that the capacitor is properly discharged and ready for the next cycle of operation.

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