How Long Does It Take for Charge to Reach 1/e of Maximum in an RC Circuit?

AI Thread Summary
To determine the time for the charge on a capacitor in an RC circuit to reach 1/e of its maximum value, the relevant equation is q = Q_final[1-e^(-t/RC)]. The maximum charge, qmax, occurs as time approaches infinity. To find the time when the charge reaches 1/e of qmax, replace q with qmax/e in the equation and solve for t. The confusion arises from miscalculating or misunderstanding the relationship between qmax and Q_final, which are indeed equal. Clarifying these concepts and correctly applying the formula will lead to the right solution.
auslmar
Messages
10
Reaction score
0

Homework Statement



A 1.47 micro F capacitor is charged through a 123 Ohm resistor and then discharged through the same resistor by short-circuiting the battery.

While the capacitor is being charged, find the time for the charge on its plates to reach 1/e of its maximum value.

Homework Equations



q = Q_final[1-e^(-t/RC)], (q)/(Q_final) = [1-e^(-t/RC)]


The Attempt at a Solution



Firstly, forgive my ignorance.

Well, I know that when charging an RC-circuit, the current decreases exponentially with time and the charge on the capacitor increases with time as the capacitor charges. Using the above equation, I assume we should be able to calculate a time constant, when t = RC, so that the charge would be 1-1/e of its final value. Though this will probably be straightforward to everyone else here, it's still not clear for me how to approach this. If I straightforwardly find the product of the capacitance and resistance, I'm only finding the aforementioned 1-1/e of the maximum value, correct? I'm beginning to become very muddled about this problem, and I can't tell if I'm fudging the the math (perhaps I just need an Algebra problem-solving review), or if my conception of the problem is way off. If anyone can provide a suggestions or hints as of how to approach this problem, I would greatly appreciate it. I apologize if this has been a waste of your time.

Thanks,

Austin
 
Physics news on Phys.org
First off, they're asking you to find 1/e of qmax. If you look at the equation you've typed out, the max value is when t is infinity (or a very large amount of time compared to the rest of the quantities). This gives you qmax.

Then replace q by qmax*1/e in the same equation and calculate the time required from that.
 
chaoseverlasting said:
First off, they're asking you to find 1/e of qmax. If you look at the equation you've typed out, the max value is when t is infinity (or a very large amount of time compared to the rest of the quantities). This gives you qmax.

Then replace q by qmax*1/e in the same equation and calculate the time required from that.

Okay. Would this mean that q_max and Q_final are equal? I'm inclined to say no because I keep reaching the same (wrong) calculation. I can't figure out any way to find them without eliminating them from both sides of the equation. I keep getting that t=RC, which I know is wrong. What am I not understanding?
 
Thanks for your help, I finally figured it out. I think I was just miscalculating and making some stupid mistakes.
 
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top