When a dielectric is inserted into an isolated and charged capacitor, the stored energy decreases to 33% of its original value. What is the value of dielectric constant?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3
for an isolated capacitor, (Q = Constant)
$U =\frac{1}{2}\frac{Q^2}{C}$
When a dielectric is inserted,
$C'=KC$
So the new energy,
$U' =\frac{1}{2}\frac{Q^2}{KC}=\frac{1}{K}\left(\frac{1}{2}\frac{Q^2}{C}\right)$
$=\frac{U_0}{K}$
$U'=33\%.U_0=\frac{33}{100}U_0$
$⇒\frac{U_0}{K}=\frac{33}{100}U_0⇒K=\frac{100}{33}≃3$