Calculating Time to Discharge Capacitor to 3V

AI Thread Summary
To determine how long it takes for a capacitor to discharge to 3V, the relevant equations are T=RC and v=Vi*e^(-t/T). The user calculated T as 1.5 ms using C=1.5E-6 F and R=1E3 ohms. The voltage Vf at 3V is 12% of the initial 25V, indicating a significant discharge. The solution involves isolating t using logarithmic functions, specifically applying the inverse operations to solve the equation. Understanding the negative sign in the decay equation is crucial for accurate calculations.
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 V = V_i e^{-t/T} 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.
A = B e^{t/C}
A/B = e^{t/C}
\ln(A/B) = t/C
C\ln(A/B) = t
 
Thanking you jambaugh
 
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