How Does Inserting a Dielectric Affect Capacitor Voltage?

Click For Summary
SUMMARY

The discussion focuses on the impact of inserting a dielectric slab (K = 2.8) into a capacitor previously charged to 12.0 V. The charge remains constant during this process, leading to a decrease in voltage across the capacitor plates. Participants emphasize the use of the equations C2 = KC1 and q = CV to derive the new capacitance and voltage values. The challenge lies in setting up the calculations without knowing the initial capacitance (C1).

PREREQUISITES
  • Understanding of capacitor fundamentals and charging principles
  • Familiarity with dielectric materials and their effects on capacitance
  • Proficiency in algebraic manipulation of equations
  • Knowledge of the formulas C2 = KC1 and q = CV
NEXT STEPS
  • Study the effects of different dielectric constants on capacitor performance
  • Learn how to derive capacitance and voltage changes in capacitors with dielectrics
  • Explore practical applications of capacitors in electronic circuits
  • Investigate the relationship between charge, voltage, and capacitance in various configurations
USEFUL FOR

Students in physics or electrical engineering, educators teaching capacitor theory, and anyone interested in understanding the effects of dielectrics on capacitor behavior.

rcrx
Messages
16
Reaction score
0

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.
 
Physics news on Phys.org
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.
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
2K
Replies
3
Views
2K
Replies
5
Views
674
  • · Replies 17 ·
Replies
17
Views
3K
Replies
6
Views
3K
Replies
8
Views
2K
Replies
3
Views
2K
Replies
10
Views
4K
Replies
6
Views
2K
Replies
9
Views
3K