Rankers Physics

Capacitors: Practice Problem & Solution

A parallel plate air capacitor of capacitance $C$ is connected to a cell of emf $V$ and then disconnected from it. A dielectric slab of dielectric constant $K$, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect? (2015)
The energy stored in the capacitor decreases $K$ times
The change in energy stored is $\frac{1}{2}CV^2\left(\frac{1}{K}-1\right)$
The charge on the capacitor is not conserved
The potential difference between the plates decreases $K$ times

Solution Explained:

To solve this problem, we apply the core principles of Capacitors. Understanding the underlying formula is key to arriving at the correct answer below:

Since the battery is disconnected before inserting the dielectric slab, the capacitor is isolated and its total charge must remain conserved. Thus, the statement 'The charge on the capacitor is not conserved' is incorrect.

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