Question

Two capacitors are identical, except that one is empty and the other is filled with a dielectric (κ = 4.69). The empty capacitor is connected to a 11.0-V battery. What must be the potential difference across the plates of the capacitor filled with a dielectric so that it stores the same amount of electrical energy as the empty capacitor?

Answer 1

Capacitance of empty capacitor   

C = ε_oA / d
Energy stored in the empty capacitor    

U = (1/2 ) C V²  
  substitute C = ε_oA / d and V = 24 V

U = (1 /2 ) (ε_oA / d )(24)²  
          
Capacitance of dielectric filled capacitor   

C^' = ε_oAk / d
Energy stored in the dielectric filled capacitor    

U^' = (1 /2 ) CV²  
Substitute C^' = ε_oAk/ d and V^' = V

U^' = (1 /2 ) (ε_oAk / d)(V)²   
According to given conditions  
                                                U = U^'

(1 /2 )(ε_oA / d )(11.0)² = (1/2 ) (ε_oAk / d )(V)²   
                                 (11.0)²    = k(V)²
                                       11.0   = V (√4.69)
                                          V    = 5.08 V