Stored Energy in two Parallel Plate Capacitors

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SUMMARY

The discussion focuses on the stored energy in two parallel plate capacitors, C1 and C2, where C2 has a dielectric constant K. Initially, both capacitors are charged to a voltage V, leading to stored energies U1 = CV²/2 for C1 and U2 = KCV²/2 for C2. Upon removing the dielectric from C2, the charge remains constant, but the capacitance decreases, resulting in an increase in stored energy. The final voltage across the capacitors after the dielectric is removed is derived as Vf = (1 + K)V.

PREREQUISITES
  • Understanding of capacitor fundamentals, including capacitance and stored energy.
  • Familiarity with the formula U = CV²/2 for energy stored in capacitors.
  • Knowledge of the effect of dielectrics on capacitance and voltage.
  • Basic algebra for manipulating equations related to charge and voltage.
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  • Learn about energy conservation in electrical circuits involving capacitors.
  • Explore the relationship between charge, voltage, and capacitance in parallel circuits.
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Homework Statement


The two-parallel-plate capacitors shown, C1=C and C2=KC, have identical plate area and plate separation. The switch S is closed, connecting the capacitors to a constant voltage power supply providing a potential difference of V. The capacitors are allowed to fully charge before the switch is opened again, disconnecting the power supply.
a)After the switch is opened, what is the stored energy in each capacitor?
b) The dielectric is now pulled from the gap of C2 by an external force. What is the voltage across and the stored energy in each capacitor with the dielectric removed?

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Homework Equations



U=CV^2/2
V=Q/C

The Attempt at a Solution



a) U1=CV^2/2
U2=KCV^2/2
b) When the dielectric is removed from the capacitor, the charge Q on the capacitor remains. Since U = Q2/2C and the capacitance is initially greater by a factor equal to the dielectric constant, C = KC0, removing the dielectric lowers C and increases U. But how do I calculate how much U is increased, and the voltage?
 
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Charge on C1 = Q1 = CV.
Charge on C2 = Q2 = kCV
When the dielectric is removed, the charge Q2 in C2 remains as it is, but voltage changes.So V' = Q2/C or Q2 = C*V'
Since the capacitors are connected in parallel, the common potential is
Vf = (Q1+Q2)/2C. = (CV+kCV)/(2C) = (1+k)V.
Now find the energy in each capacitor.
 
Thankz rl.bhat.

I get U1=C1((1+k)V)^2/2
U2=C2((1+k)V)^2/2

Right?
 
Last edited:

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