Question

The potential differences that must be applied across the parallel and series combination of 3 identical capacitors is such that the energy stored in them becomes the same. The ratio of potential difference in parallel to series combination is

• A. \(\frac{1}{4}\)
• B. \(\frac{1}{6}\)
• C. \(\frac{1}{3}\)
• D. \(\frac{1}{8}\)

Hint:

For equal energy in parallel and series combinations of capacitors, the ratio of potential differences is given by the square root of the ratio of their capacitances.

Answer 1

The Correct Option is C

Step 1: Understanding the question.
We are given that the energy stored in both the parallel and series combinations of capacitors is the same. The energy stored in a capacitor is given by \( E = \frac{1}{2} C V^2 \). Since the energy is the same, we can equate the energies for both combinations.

Step 2: Analyzing the parallel and series combinations.
- In the parallel combination, the total capacitance is \( C_{parallel} = 3C \). - In the series combination, the total capacitance is \( C_{series} = \frac{C}{3} \).
Step 3: Deriving the ratio.
The potential difference across each combination must satisfy the energy condition. By equating the energies, we find that the ratio of potential differences \( \frac{V_{parallel}}{V_{series}} = \frac{1}{\sqrt{3}} \). This gives the correct answer as \( \frac{1}{3} \).