How Does Inserting a Dielectric Affect Capacitor Voltage?

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Homework Help Overview

The problem involves a capacitor initially charged by a 12.0-V battery, which is then disconnected from the battery before a dielectric material with a dielectric constant of K = 2.8 is inserted. The focus is on determining how the potential difference across the capacitor plates changes due to the introduction of the dielectric.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between charge, capacitance, and voltage, noting that the charge remains constant when the dielectric is inserted. There is uncertainty about how to mathematically set up the problem, particularly regarding the use of the formulas provided.

Discussion Status

Some participants have offered guidance on using the formulas related to charge and capacitance, suggesting that the original poster can express charge in terms of the initial capacitance and voltage. There is an ongoing exploration of how to calculate the new capacitance and voltage after the dielectric is inserted, but no consensus has been reached on a complete method.

Contextual Notes

The original poster has expressed confusion about the mathematical setup of the problem and the absence of a specific value for the initial capacitance (C1) is noted as a constraint in the discussion.

rcrx
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Homework Statement


An empty capacitor is connected to a 12.0-V battery and charged up. The capacitor is then disconnected from the battery, and a slab of dielectric material (K = 2.8) is inserted between the plates. Find the amount by which the potential difference across the plates changes.


Homework Equations


C2 = KC1
q = CV


The Attempt at a Solution


I know that the charge will stay the same and voltage will drop.

I have no idea how to set this up mathematically. This is where I have hit a road block.
 
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You are not give C1, so you must think of it as a "known" that may appear in the answer. From that and one of your formulas, you can calculate the charge.

Great observation to see that the charge remains the same with the dialectric is inserted!

Use the formula with the V in it to find the potential on the cap with dielectric.
 
Thanks for the reply. But how do I set it up? I am so confused. I know it is simple, but some problems I just can't wrap my head around mathematically.

Any and all help is very much appreciated!
 
Well, to calculate the charge, I just meant to use your formula q = CV.
To avoid confusion, I would replace C with C1. Put in your potential and you've got an expression for q with no unknowns (except C1, which we are treating as a known for now).

The first formula gives the new C2.
Use the 2nd formula again to find the new V.
 

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