Q128 / 150 · MHT CET 2026 (11 April Shift 2) · Physics
Initially, 'n' identical capacitors are joined in parallel, are charged to potential 'V'. Now they are separated and joined in series. Then
- Apotential difference and total energy of the combination remain the same
- Bpotential difference remains the same and energy increases 'n' times
- Correct answerCpotential difference becomes 'nv' and energy remains the same
- Dpotential difference is 'nv' and energy increases 'n' times.
Solution
Initial capacitance of each capacitor is $C$.
In parallel combination, the potential difference across each capacitor is $V$.
Charge on each capacitor, $q = CV$.
Total initial energy, $U_i = n \times \dfrac{1}{2}CV^2$.
When the capacitors are separated and connected in series, the charge on each capacitor remains $q = CV$.
The potential difference across the series combination is the sum of individual potential differences.
$V_f = V + V + \dots \text{n times} = nV$.
Equivalent capacitance in series, $C_s = \dfrac{C}{n}$.
Total final energy, $U_f = \dfrac{1}{2}C_s V_f^2 = \dfrac{1}{2} \left(\dfrac{C}{n}\right) (nV)^2 = n \times \dfrac{1}{2}CV^2$.
Thus, $U_f = U_i$.
The potential difference becomes $nV$ and the total energy remains the same.
Answer: potential difference becomes 'nv' and energy remains the same
In parallel combination, the potential difference across each capacitor is $V$.
Charge on each capacitor, $q = CV$.
Total initial energy, $U_i = n \times \dfrac{1}{2}CV^2$.
When the capacitors are separated and connected in series, the charge on each capacitor remains $q = CV$.
The potential difference across the series combination is the sum of individual potential differences.
$V_f = V + V + \dots \text{n times} = nV$.
Equivalent capacitance in series, $C_s = \dfrac{C}{n}$.
Total final energy, $U_f = \dfrac{1}{2}C_s V_f^2 = \dfrac{1}{2} \left(\dfrac{C}{n}\right) (nV)^2 = n \times \dfrac{1}{2}CV^2$.
Thus, $U_f = U_i$.
The potential difference becomes $nV$ and the total energy remains the same.
Answer: potential difference becomes 'nv' and energy remains the same
Hence, the correct answer is option: 'C'.