Question

A parallel plate condenser with a dielectric constant $K$ between the plates has a capacity $C$ and is charged to a potential $V$ volt. The dielectric slab between the plates is slowly removed and then reinserted. The net work done by the system in this process is

• A. Zero
• B. $\frac{1}{2}( K -1) CV ^{2}$
• C. $\frac{ CV ^{2}( K -1)}{ K }$
• D. $(K-1) C V^{2}$

Answer 1

Answer: (A)

Q is constant
Case-I

$C'=k C$
$Q=$ same
$U _{1}=\frac{ Q ^{2}}{2 C '}=\frac{ Q ^{2}}{2 kC }$
Case-II

$C ''= C$
$Q =$ same
$U _{2}=\frac{ Q ^{2}}{2 C }$
Case-III

$C '''= kC$
$Q =$ same
$U _{3}=\frac{ Q ^{2}}{2 k C }$
Work done $= U _{3}- u _{1} =0$