Capacitors and Dialectric Constant

In summary, the time constant for the first circuit is RC, and the time constant for the second circuit is 1/RC.
  • #1
kris24tf
35
0
Capacitors, Hard Problem

Four identical capacitors are connected with a resistor in two different ways. When they are connected as in part a of the drawing, the time constant to charge up this circuit is 0.67 s. What is the time constant when they are connected with the same resistor as in part b?

The pictures included are http://edugen.wiley.com/edugen/courses/crs1000/art/qb/6e/ch20p_99.gif

I really have no idea what I'm doing here. My work is as follows:

T=RC
Ta=RCa, Tb=RCb
Ca=Cs1+Cs2
1/Cs=1/C+1/C
1/2/C=1/2C=2C
1/Cb=1/Cp+1/C
Cb=1/(1/Cp+1/C)
Cp=C+C=2C
Cb=1/(3/2C)=s/3C
Ta=R(2)(C)
Tb=R(2/3)(C)
Tb/Ta=R(2)(C)/R(2/3)(C)
Tb=3Ta

If anyone could help me with what I did wrong/what I need to fix, I'd appreciate it
 
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  • #2
I didn't work through your equations, but basically you need to calculate the total capacitance in each situation to determine the RC time constant.

For the first circuit, the total combination of capacitance is C, right? Each leg is half of C, and the two parallel C/2 legs together gives you back a whole C, right? So the time constant for the first circuit is RC.

You need to then calculate the total combination of capacitance for the second circuit. The two caps in parallel are easy -- what is the combination of the two C caps in parallel? And then you end up with 3 caps in series -- the combo of the two parallel caps, plus the two C caps. What is the equation for combining caps in series? Just combine the equivalent capacitance from the two parallel C caps and the other two series C caps, and you will get an equivalent total capacitance. That will give you the relative time constant compared to the original RC from the first circuit. Makes sense?
 
  • #3
I'm still confused. I tried working through what you said but I don't come up with anything...
 
  • #4
You've got parts of it right in the work that you showed.

What is the equivalent capacitance of the caps in the first circuit arrangement? (parallel combo of two series C)

What is the equivalent capacitance of the caps in the second circuit arrangement? (two parallel C then in series with two other C)

What is the ratio between these two equivalent capacitance values? That will be the ratio of the time constants...
 

FAQ: Capacitors and Dialectric Constant

What is a capacitor?

A capacitor is an electronic component that stores electrical energy in the form of an electric field. It is made up of two conducting plates separated by a non-conducting material, called a dielectric.

How does a capacitor work?

A capacitor works by accumulating and storing electrical charge on its conducting plates. When a voltage is applied to the capacitor, one plate becomes positively charged and the other becomes negatively charged. The dielectric material between the plates prevents the charges from flowing together, thus storing the electrical energy.

What is the role of a dielectric in a capacitor?

A dielectric is the non-conducting material between the conducting plates of a capacitor. Its main role is to increase the capacitance, or the ability of the capacitor to store charge, by reducing the electric field between the plates. Dielectric materials also provide insulation and prevent the charges from leaking out.

What is the dielectric constant of a material?

The dielectric constant, also known as relative permittivity, is a measure of a material's ability to store electrical energy in an electric field. It is the ratio of the capacitance of a capacitor with the dielectric material to the capacitance of the same capacitor with a vacuum as the dielectric. A higher dielectric constant means the material is better at storing charge.

How does temperature affect the dielectric constant of a material?

The dielectric constant of a material can change with temperature. Generally, the dielectric constant decreases as temperature increases. This is because at higher temperatures, molecules in the dielectric material have more thermal energy to move and vibrate, disrupting the electric field and reducing the ability to store charge. However, some materials may have a constant or even increasing dielectric constant with temperature due to their unique molecular structure.

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