When capacitors are connected in series across DC voltage then_____

• A. The same current flows through each capacitor in a given time
• B. The voltage across each capacitor is the same
• C. The charge on each capacitor is the same
• D. The charge on each capacitor is the same and the same current flows through each capacitor in a given time

Answer: (D)

When voltage is applied across the capacitor one plate becomes negatively charged with electrons leaving the battery. At the same time, electrons leave the other plate to resupply the battery, leaving that plate positively charged. This effect is called polarisation. The current flows until the charge across the capacitor is equal to the battery emf, at which point everything stops.
In series connections, the same charging current flows through all capacitors as soon as a voltage is applied. Hence in a series connection same current flows through each capacitor.