Calculate time for capacitor to charge and discharge

In summary, the conversation discusses the concept of charging and discharging a capacitor and the use of the 5τ approximation to determine when the capacitor is considered "fully" charged. There is also a mention of using LaTeX for math equations.
  • #1
Edy56
38
5
Homework Statement
Is the capacitor C= 10μF in the circuit unpolarized or polarized? When the switch is in position (1), the capacitor is charged, and when it is in position (2), the capacitor is discharged. Determine the time required to fully charge the capacitor and the time required to fully discharge the capacitor. It is known: V= 10 V, R1= 15 kΩ, R2= 56 kΩ, R3= 7 kΩ
Relevant Equations
None
I really don't get this one. Why do I need V? Since I didn't use it, I assume my work Is incorrect.
IMG_20230604_235520_1.jpg
 
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  • #2
Seems like a trick question; are you sure you copied it exactly? It takes an infinite amount of time to "fully" charge or discharge a capacitor (that's the nature of the exponential funtion).

Also, please learn to use LaTeX to post math equations. There is a link to the "LaTeX Guide" below the Edit window. Thank you kindly. :smile:
 
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  • #3
berkeman said:
Seems like a trick question; are you sure you copied it exactly? It takes an infinite amount of time to "fully" charge or discharge a capacitor (that's the nature of the exponential funtion).

Also, please learn to use LaTeX to post math equations. There is a link to the "LaTeX Guide" below the Edit window. Thank you kindly. :smile:
It looks like they are using the ##5\tau ## approximation.
 
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  • #4
erobz said:
It looks like they are using the ##5\tau ## approximation.
Ahh, the old ##5\tau## approximation for ##\infty## -- got it. :wink:
 
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  • #5
You don't need V as long as the criteria for "fully" is a percentage of V, as with the 5τ approximation, which is essentially a 99% done criterion.
 
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  • #6
DaveE said:
You don't need V as long as the criteria for "fully" is a percentage of V, as with the 5τ approximation, which is essentially a 99% done criterion.
Thank you.
 
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FAQ: Calculate time for capacitor to charge and discharge

What is the formula to calculate the charging time of a capacitor?

The charging time of a capacitor in an RC circuit can be calculated using the formula \( V(t) = V_0 \left(1 - e^{-t/RC}\right) \), where \( V(t) \) is the voltage across the capacitor at time \( t \), \( V_0 \) is the supply voltage, \( R \) is the resistance, and \( C \) is the capacitance. The time constant \( \tau \) is given by \( \tau = RC \). The capacitor is considered fully charged after about 5 time constants (5τ).

How do you calculate the discharging time of a capacitor?

The discharging time of a capacitor can be calculated using the formula \( V(t) = V_0 e^{-t/RC} \), where \( V(t) \) is the voltage across the capacitor at time \( t \), \( V_0 \) is the initial voltage across the capacitor, \( R \) is the resistance, and \( C \) is the capacitance. Similar to charging, the capacitor is considered fully discharged after about 5 time constants (5τ).

What is the time constant in an RC circuit?

The time constant, denoted by the Greek letter \( \tau \) (tau), is a measure of the time it takes for the voltage across the capacitor to either charge up to about 63.2% of its final value or discharge to about 36.8% of its initial value. It is calculated as \( \tau = RC \), where \( R \) is the resistance and \( C \) is the capacitance.

How long does it take for a capacitor to fully charge or discharge?

In practical terms, a capacitor is considered to be fully charged or discharged after about 5 time constants (5τ). This means that the voltage across the capacitor will be very close to its final value, with less than 1% deviation.

What factors affect the charging and discharging time of a capacitor?

The charging and discharging time of a capacitor are primarily affected by the resistance \( R \) and the capacitance \( C \) in the circuit. The time constant \( \tau \), which is the product of \( R \) and \( C \), determines how quickly the capacitor charges or discharges. Higher resistance or capacitance values result in a longer time constant and thus a slower charging or discharging process.

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