In summary, adding a dielectric between the plates of one of the two identical capacitors in Fig. 25-23 results in the following changes: for the first capacitor with the dielectric, the potential decreases while the charge and capacitance increase. For the second capacitor without the dielectric, the potential increases while the charge stays the same and the capacitance remains unchanged. The reason for these changes is due to the decrease in electric field between the plates of the first capacitor with the dielectric, leading to a decrease in potential and increase in charge and capacitance. Both capacitors are in series, so the charge on both capacitors must be the same, but the potential and capacitance can vary. These changes satisfy Kirchhoff
  • #1
Nemo_Sol
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Problem: When a dielectric slab is inserted between the plates of one of the two identical capacitors in Fig. 25-23, do the following properties of that capacitor increase, decrease, or remain the same: (a) capacitance, (b) charge, (c) potential difference (d) How about the same properties of the other capacitor?

CAPACITOR 1 = CAPACITOR WITH DIELECTRIC |CAPACITOR 2 = CAPACITOR WITHOUT DIELECTRIC(ABOVE CAPACITOR 1 IN THE DIAGRAM)

I said that the potential of the first capacitor decreases and that the charge it stores also increases. For the 2nd capacitor, I said it's capacitance would decrease. I'm not so sure though, I think it may stay the same as well?
Potential would increase and charge would increase for the 2nd capacitor as well
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Attempt at Solution: The main problem I'm having at solving this is the fact that both charge and voltage for the individual capacitors are variable. Please explain the situation and why the values for potential, capacitance and charge either decrease, increase or stay the same.

What I think: When a dielectric is added, E between the capacitor decreases by a factor of k so voltage must decrease for the first capacitor and thus the voltage for the 2nd capacitor must increase by the same amount to fulfill Kirchhoff's laws.

Adding a dielectric also allows for a capacitor to store more charge at the same potential so the first capacitor must store more charge since c = q/v <- direct relationship.

I'm confused on what happens to the 2nd capacitor. They're in series so there's that inverse relationship and total capacitance decreases.
 
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  • #2
Try this: start with the "truths" you know. Eg: 1) kirchhoffs rule is always valid, 2) the capacitors are in series so the effective capacitance can be found, 3) because they are in series the charge on both of them at any instant has to be the same thought the value of this charge could vary, 4) again because they are in series we can find a relation between their V1 and v2. These relations should help you come to the conclusions.

Here is what I got :
Capacitor 1 (one with dielectric): Q decreases, C increases, V decreases
Capacitor 2: Q decreases, V increases, C does not change.
I'm fairly sure I'm correct and they seem to satisfy all the equations too qualitatively.
 

1. What is a capacitor?

A capacitor is an electronic component that stores electrical charge. It consists of two conductive plates separated by an insulating material, or dielectric.

2. What is a series circuit?

A series circuit is a circuit in which the components are connected in a single loop, with the same amount of current flowing through each component.

3. How does a capacitor work in a series circuit?

In a series circuit, the capacitors are connected end to end, or in series. This means that the positive plate of one capacitor is connected to the negative plate of the next capacitor. The dielectric material between the plates allows for the buildup of charge, increasing the overall capacitance of the circuit.

4. What is the effect of adding a dielectric to a series circuit?

Adding a dielectric to a series circuit increases the overall capacitance of the circuit. This is because the dielectric material reduces the electric field between the plates, allowing for more charge to be stored on the plates.

5. What are some practical applications of capacitors in a series circuit with a dielectric?

Capacitors in a series circuit with a dielectric are commonly used in electronic devices to store energy and regulate voltage. They are also used in power supplies, audio equipment, and electronic filters.

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