Ch 24: Capacitors & DielectricsWorksheetSee all chapters
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Concept #1: Intro To Dielectrics

Practice: A capacitor in a vacuum is charged to 64V between its plates, then disconnected. Initially, each plate has 32μC. An insulating slab of dielectric glass with k = 3 is placed between the platesa) What is the capacitor’s new capacitance? b) What is the new voltage across the capacitor?

Practice: A parallel plate capacitor is formed by bringing two circular plates, of radius 0.5 cm, to a distance of 2 mm apart. The capacitor is made so that it has a dielectric of constant between the plates. When the charge on the capacitor is 3 nC, the voltage of the capacitor is 5000 V. What is the dielectric constant?

Example #1: Partial Dielectrics


Hey guys. Let's do an example. what is the new capacitance of the two capacitors that are partially filled with dielectrics shown in the following figure, okay? We have an A and B situation going on here. So, let's just address them each distinctly, okay? For Part A, we have a dielectric that fills the top half of this capacitor, what this is going to be like is, this is going to be like two capacitors in parallel, sorry, in series, okay? Imagine, if this was plus Q then we'd have a minus Q here on the inner surface of this dielectric, a plus Q on the outer surface of the dielectric, and a minus Q on this plate. So, this looks like a single capacitor and this looks like a single capacitor, where the upper capacitor has a dielectric and the lower capacitor does not, we'll call those C1 and C2. So, C1 is going to be Kappa, Epsilon naught, the area is a but the distance is d over 2, so this is 2 Kappa, Epsilon naught, A over d, once I rearrange it, C2 is not going to have any dielectric. So, no Kappa it's epsilon naught, the area is still A and the distance is still d over 2, so this is 2 epsilon naught A over d. Now, since these are in series, then I would say the equivalent capacitance, so the total capacitance of this physical capacitor is 1 over C equals 1 over 2 Kappa epsilon naught naught, A over d plus 1 over 2 epsilon naught A over d, okay? The least common denominator is 2 Kappa epsilon naught, A over d. So, I need a Kappa over a Kappa, so this is going to be 1 plus Kappa over 2 Kappa epsilon naught A over d, okay? So, the whole thing is going to be, let me give myself just a little bit of room here, C equals to Kappa over 1 plus Kappa Epsilon naught, A over d. Now, this coefficient right here looks kind of like an effective dielectric constant, right? Like, if you put half of a dielectric through then this looks almost like its own dielectric constant, right? That's just a number times epsilon, epsilon naught, A over V, sorry, it's just a number times the capacitance, so it looks like it's effective dielectric constant, okay?

Now, let's do Part B this time, we put a dielectric halfway through on the left side. Now, what's the same here is going to be the potential difference or the voltage, that's just going to be whatever it is across the plates whether or not the dielectric is there, okay? So, these look like they are in parallel, right? They both have the same voltage. So, let's find, I'll call this one C1 I'll call this 1 C2, let's find those capacitances, C1 is going to be Kappa Epsilon naught, what's the area though? Well, it has half of the capacitor so it has half of the area, so this is a over 2 but the distance is the same, so this is, we'll call it Kappa over 2, epsilon naught, A over d, c2 is just going to be epsilon naught, no Kappa, right? Because it's in a vacuum, the area once again is 1/2, it has half the capacitor, so this is A over 2 d, this is just 1/2 epsilon naught A over d. Now, these are in parallel so I can just add them, okay? Once I've added them we get this, one half, this k over 2 plus this 1 over 2, they have the same denominator. So, I can just say it's k plus 1 over 2 and notice this also looks like a normal capacitor but with some sort of weird dielectric constant, but either way, this is the capacitance for Part B. Alright guys, thanks for watching.

A parallel plate capacitor has a measured capacitance of 1.0 pF, and is charged to 2.0 μC, then disconnected from the power supply. The space between the plates is then filled with a certain dielectric material with a dielectric constant of K = 4.0. What is the resulting capacitance and the stored electric potential energy? A) 4.0 pF and 1.0 J B) 0.25 pF and 0.5 J C) 4.0 pF and 0.5 J D) 4.0 pF and 4.0 J
The figure below shows four parallel plate capacitors: A, B, C, and D. Each capacitor carries the same charge q and has the same plate area A. As suggested by the figure, the plates of capacitor A and C are separated by a distance  d while those of B and D are separated by a distance 2d. Capacitors A and B are maintained in vacuum while capacitors C and D contain dieelctrics with constant k = 5. Which list below places the capacitors in order of  increasing capacitance?  A) A, B, C, D B) B, A, C, D C) A, B, D, C D) B, A, D, C E) D, C, B, A
A parallel-plate capacitor is connected to a battery and allowed to charge up. While still connected to battery, a dielectric material is then inserted between two plates of the capacitor. What can we say about the new charges on the capacitor plates? A) The total charges increases B) The total charges decreases C) The total charges remains the same D) Unable to determine from the information given
A parallel plate capacitor has plates with area A = 350cm2 separated by a distance d = 1.5mm. A dielectric with dielectric constant K = 3.1 is inserted between the two plates. What is the capacitance now?
A stack of paper with net dielectric constant K is placed between the plates of a capacitor holding a fixed charge. What happens to the electric field F and the energy U stored between the plates (E0 and U0 are the values before sheet is inserted)? A. E → E0/K, U → U0/K B. E → E0/K, U → U0K C. E → E0K, U → U0K D. E → E0K, U → U0/K E. E → E0, U → U0/K2
The effective area of each plate of parallel plate capacitor is 2.1 m2. The capacitor is filled with neoprene rubber (k = 6.4). When a 6.0-V potential difference exists across the plates of the capacitor stores 4.0 µC of charge. Determine the plate separation of capacitor.