When capacitors are connected in series across a potential difference, there is a loss in their stored energy because:

Analyze the question: It asks why there is a "loss in stored energy" when capacitors are connected in series across a potential difference. We need to find the reason that best fits.

Concept:

• For capacitors in series, the equivalent capacitance is 1/C_total = 1/C₁ + 1/C₂ + ... so C_total is always smaller than the smallest individual capacitor.
• Energy stored in a capacitor connected to a fixed voltage V is E = ½ C_total V²
• Since V is fixed (the supply voltage), the energy depends directly on C_total.

Working:

1. Take two capacitors, each of capacitance C, in series across V.
2. C_total = C/2.
3. Energy stored in series: E_series = ½ (C/2) V² = ¼ CV².
4. If the same two capacitors were connected in parallel instead: C_total = 2C, so E_parallel = ½ (2C) V² = CV².
5. Compared with a single capacitor, or with the parallel arrangement, the series arrangement stores less energy, and this is because the overall capacitance has decreased.

Checking the other options:

• A: Internal resistance of the source does not determine the final stored energy (it only affects how fast charging occurs).
• B: In series, the charges on the capacitors are equal, not unequal. This option is false.
• C: Charge flow between capacitors is what causes energy loss when capacitors with different voltages are connected in parallel, not in series.
• D: The decrease in overall capacitance reduces E = ½ C_total V².

Answer: D. Decrease in the overall capacitance of the capacitors.

Exam tip: Remember "Series capacitors: capacitance goes down, so stored energy at fixed V goes down." Series capacitors behave like parallel resistors (the total is smaller than the smallest), and the same charge Q sits on each capacitor.