Calculating Capacitance for Optimal Light-Bulb Performance

[EzequielSeattle]

Homework Statement

Imagine that you have a light-bulb that has a resistance of about 10 ohms and that can tolerate a maximum voltage of 3 volts. Imagine that you want to connect this to a charged capacitor large enough to keep the bulb glowing reasonably brightly for more than 10 seconds. Roughly what should the capacitor's capacitance be?

Homework Equations

V_C(t) = V₀e^(-t/RC)

The Attempt at a Solution

I feel as if I need another equation for this problem, because I don't have 4 variables to plug in! The starting potential of the capacitor should be 3 volts, right?

So

V_C(t) = (3 volts)e^{(-10 seconds/(10 ohms)*C)}

So now I have unknowns of C and V_C, and I need to solve for C. Clearly I'm missing something, but I'm not sure what... Can somebody point me in the approximately right direction? Thank you!

 

[berkeman]

Homework Statement

Imagine that you have a light-bulb that has a resistance of about 10 ohms and that can tolerate a maximum voltage of 3 volts. Imagine that you want to connect this to a charged capacitor large enough to keep the bulb glowing reasonably brightly for more than 10 seconds. Roughly what should the capacitor's capacitance be?

Homework Equations

V_C(t) = V₀e^(-t/RC)

The Attempt at a Solution

I feel as if I need another equation for this problem, because I don't have 4 variables to plug in! The starting potential of the capacitor should be 3 volts, right?

So

V_C(t) = (3 volts)e^{(-10 seconds/(10 ohms)*C)}

So now I have unknowns of C and V_C, and I need to solve for C. Clearly I'm missing something, but I'm not sure what... Can somebody point me in the approximately right direction? Thank you!

Good start. :-)

I would probably start with the equation $$I = C \frac{dV}{dt}$$

 

[mfb]

The light-bulb will get dimmer as the voltage goes down, but it should not get too dim. You can define what exactly that means by fixing V_c(10s) to some reasonable value.

 

[EzequielSeattle]

So I can arbitrarily say that V_c(10 s) is, say, 1.5 volts? And then solve for C, which would give 1.4 farads. Isn't that considered a really really high capacitance?

 

[EzequielSeattle]

Would dV/dt just be the derivative of the right side of my equation above? That is, dV/dt = -(V₀/RC)*e^-t/RC?

Then, since I = C*dV/dt,

I = -3 volts/10 ohms * e^{(10 s)/((10 ohms)*C)}

I feel like that doesn't help, because then I just have another unknown (I).

 

[mfb]

So I can arbitrarily say that V_c(10 s) is, say, 1.5 volts?

Right.

And then solve for C, which would give 1.4 farads. Isn't that considered a really really high capacitance?

Maybe 20 years ago, but now those are cheap elements available everywhere.