A parellel plate capacitor with plate speration d is charged with a battery so that energy stored is #"U"#. If a plate of dielectric #"K"# and thickness d is placed betweeen the plates of capacitor and battery remains connected. The work by battery is?

Options:

  1. #"KU"#

  2. #"2U(K - 1)"#

  3. #"U(K - 1)"#

  4. #"2KU"#

1 Answer
Mar 14, 2018

#2U(K-1)#

Explanation:

The energy stored in a capacitor is given by #U = 1/2 CV^2# where #C# is the capacitance and #V# is the potential.

When the dielectric is introduced, the capacitance increases by a factor of #K#, but since the battery is still connected, the potential #V# does not change.

So, the charge stored in the capacitor grows from #CV# to #K times CV#. The battery must pump in this extra charge #(K-1)CV# at the constant voltage #V# - and the work it must do for this is
#(K-1)CV times V = (K-1)CV^2=2(K-1)U#

Note that this is twice the energy gained by the capacitor.