Question

A parallel plate capacitor is charged by connecting a 2 Volt battery across it. It is then disconnected from the battery and a glass slab is introduced between plates. Which of the following pair of quantities decrease ?

• A. Energy stored and capacitance
• B. Charge and potential difference
• C. Capacitance and charge
• D. Potential difference and energy stored

Answer 1

The Correct Option is D

Let's analyze the scenario of a capacitor being charged, disconnected, and then subjected to a dielectric material (glass slab) between its plates. Based on this analysis, we need to determine which pair of quantities decreases.

Step 1: Charging the Capacitor

The capacitor is charged by connecting a 2 Volt battery across it. Initially, the potential difference \( V \) across the capacitor is 2 Volts. As the voltage is applied, the charge \( Q \) stored on the plates increases.

Step 2: Disconnecting the Battery

After disconnecting the battery, the potential difference \( V \) across the capacitor remains the same as it was when charged, i.e., 2 Volts. The charge \( Q \) remains the same because there is no current flow, and the capacitor is isolated from the battery.

Step 3: Introducing the Glass Slab (Dielectric Material)

When a dielectric material, such as a glass slab, is introduced between the plates of the capacitor, it increases the capacitance \( C \) of the capacitor. The capacitance with the dielectric is given by the formula:

\( C = k \cdot C_0 \)

Where:

• k: The dielectric constant of the material (for glass, typically \( k > 1 \))
• C₀: The original capacitance of the capacitor without the dielectric

As the capacitance increases due to the introduction of the glass slab, the charge \( Q \) stored on the plates also increases to maintain the same potential difference \( V \). This is because the relationship between charge, capacitance, and voltage is given by:

\( Q = C \cdot V \)

Conclusion:

Based on the analysis, we can conclude that the correct pair of quantities that decreases is:

• Potential difference and energy stored.

Correct answer: (D) Potential difference and energy stored.