Capacitors And Capacitance

We are given two capacitors, (air capacitor) and (capacitor filled with a dielectric medium of dielectric constant 5), connected in series to a voltage source of 12V.

The voltage across each capacitor in a series combination is inversely proportional to their capacitances. The total capacitance of capacitors in series is given by:

For , the capacitance is that of an air capacitor, and for , the capacitance increases due to the dielectric medium. The capacitance of is given by:

Substitute into the total capacitance equation:

Thus, the total capacitance is:

Now, the voltage drop across each capacitor is proportional to the inverse of its capacitance. The voltage drop across is:

And the voltage drop across is:

Thus, the voltage drops across the two capacitors are:

• Across :
• Across :

Correct Answer:

Correct Answer: (1) 2V and 10V

Given:

• N capacitors, each with capacitance
• Connected in parallel to store total charge
• Potential across each capacitor

Step 1: Determine Number of Capacitors (N)

In parallel connection, total capacitance .

Total charge stored:

Substitute values:

Step 2: Calculate Equivalent Capacitance in Series

When these N capacitors are connected in series:

Conclusion:

The equivalent capacitance in series is .

Answer: