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A parallel plate capacitor without a dielectric is charged up so that it stores potential energy Uo, and it is then disconnected so that its charge remains the same. A dielectric with constant k = 2 is then inserted between the plates. What is the new potential energy stored in the capacitor with the dielectric? a) 400 b) 200 c) U. d) 14U

Answer :

Answer:

[tex] \frac{U_{o}}{2}[/tex]

Explanation:

Q = Amount of charge stored by parallel plate capacitor

C₀ = Capacitance of the capacitor

U₀ = Amount of electric potential energy stored

Amount of electric potential energy stored is given as

[tex]U_{o} = \frac{Q^{2}}{2C_{o}}[/tex]

k = dielectric constant of dielectric = 2

New capacitance of the capacitor is given as

C = k C₀

New amount of electric potential energy stored is given as

[tex]U = \frac{Q^{2}}{2C}[/tex]

[tex]U = \frac{Q^{2}}{2 k C_{o}}[/tex]

[tex]U = \frac{U_{o}}{k}[/tex]

[tex]U = \frac{U_{o}}{2}[/tex]

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