Calculating Time to Discharge Capacitor to 3V

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Homework Help Overview

The discussion revolves around calculating the time it takes for a capacitor to discharge to a voltage of 3V, given specific values for capacitance, resistance, and initial voltage. The subject area includes circuits and capacitor discharge behavior.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of the equation v=Vi*e^(t/T) to determine the discharge time and express confusion regarding the application of this formula. There are questions about whether to solve for time directly or to use a normalized time constant curve for estimation.

Discussion Status

Some participants have provided algebraic manipulations to isolate time in the discharge equation, while others are still exploring their understanding of the problem and the implications of the negative sign in the equation. There is no explicit consensus on the best approach yet.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. The original poster expresses difficulty in solving for time, indicating potential gaps in understanding the underlying concepts.

Rupturez
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Homework Statement


Determine how long it takes the capacitor to discharge to a value of 3v
C=1.5E-6F
R=1E3ohms
Vi=25v
Vf=3v


Homework Equations


T=RC
v=Vi*e^(t/T)



The Attempt at a Solution


T=1000*1.5E-6
T=1.5E-3s

Vf(3v) is 12% of the initial 25v

Im having trouble solving for time with this equation v=Vi*e^(t/T)

many thanks in advance
 
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Should I be solving for t or using a normalised universal timeconstant(RC) curve to estimate time?
 
Rupturez said:

Homework Statement


Determine how long it takes the capacitor to discharge to a value of 3v
C=1.5E-6F
R=1E3ohms
Vi=25v
Vf=3v


Homework Equations


T=RC
v=Vi*e^(t/T)



The Attempt at a Solution


T=1000*1.5E-6
T=1.5E-3s

Vf(3v) is 12% of the initial 25v

Im having trouble solving for time with this equation v=Vi*e^(t/T)

many thanks in advance

Firstly [itex]V = V_i e^{-t/T}[/itex] there's a negative sign reflecting the decay of the voltage... it doesn't grow!

Secondly solving this for t is basic algebra, apply inverse operations until you isolate t.
[itex]A = B e^{t/C}[/itex]
[itex]A/B = e^{t/C}[/itex]
[itex]\ln(A/B) = t/C[/itex]
[itex]C\ln(A/B) = t[/itex]
 
Thanking you jambaugh
 

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