CUET · PHYSICS · PYQ PAPER 2023
\(n _1\) identical capacitors, each of capacitance \(C _1\), are connected in series and charged by a source of potential difference \(3 V . n _2\) identical capacitors, each of capacitance \(C_2\), are connected in parallel and charged by a source of potential difference 2 V . Total energy stored in both the combinations is the same. What is the value of capacitance \(C _2\) in terms of \(C _{ 1 }\) ?
- A \(\frac{4 C_1}{9 n_1 n_2}\)
- B \(\frac{9 C_1}{4 n_1 n_2}\)
- C \(\frac{9 C_1}{2 n_1 n_2}\)
- D \(\frac{9 C_1}{8 n_1 n_2}\)
Answer & Solution
Correct Answer
(B) \(\frac{9 C_1}{4 n_1 n_2}\)
Step-by-step Solution
Detailed explanation
\(C_{eq1} = \frac{C_1}{n_1}\) \(E_1 = \frac{1}{2} C_{eq1} V_1^2 = \frac{1}{2} \left(\frac{C_1}{n_1}\right) (3 V)^2 = \frac{9 C_1}{2 n_1}\) \(C_{eq2} = n_2 C_2\) \(E_2 = \frac{1}{2} C_{eq2} V_2^2 = \frac{1}{2} (n_2 C_2) (2 V)^2 = 2 n_2 C_2\)…
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