Problem with Capacitance

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In summary: This is not a big capacitor by modern standards.In summary, the conversation discusses using a light-bulb with a resistance of 10 ohms and a maximum voltage of 3 volts, connected to a charged capacitor, to keep the bulb glowing for more than 10 seconds. The relevant equation is VC(t) = V0e(-t/RC) and the problem can be solved by setting an arbitrary value for Vc(10s) and solving for C. The resulting capacitance is considered relatively small by modern standards.
  • #1

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


VC(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

VC(t) = (3 volts)e(-10 seconds/(10 ohms)*C)

So now I have unknowns of C and VC, 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!
 
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  • #2
EzequielSeattle said:

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


VC(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

VC(t) = (3 volts)e(-10 seconds/(10 ohms)*C)

So now I have unknowns of C and VC, 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 [tex]I = C \frac{dV}{dt}[/tex]
 
  • #3
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 Vc(10s) to some reasonable value.
 
  • #4
So I can arbitrarily say that Vc(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?
 
  • #5
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).
 
  • #6
EzequielSeattle said:
So I can arbitrarily say that Vc(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.
 

1. What is capacitance?

Capacitance is a measure of the ability of an object to store electrical charge. It is typically represented by the letter C and is measured in units of farads (F).

2. What causes problems with capacitance?

Problems with capacitance can be caused by a variety of factors, including the type and quality of the materials used, the design of the circuit, and external factors such as temperature and humidity.

3. How can capacitance be calculated?

The formula for calculating capacitance is C = Q/V, where C is capacitance, Q is charge, and V is voltage. It can also be calculated by measuring the physical characteristics of the capacitor, such as the distance between the plates and the type of dielectric material used.

4. What are some common symptoms of capacitance problems?

Some common symptoms of capacitance problems include unexpected fluctuations in voltage or current, unstable circuit behavior, and the inability of a capacitor to hold a charge.

5. How can capacitance problems be solved?

The solution to capacitance problems will depend on the specific cause. It may involve replacing faulty components, redesigning the circuit, or adjusting external factors such as temperature and humidity. In some cases, it may be necessary to use different types of capacitors with different capacitance values.

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