In a series combination of capacitors connected across a battery

The correct option is: each capacitor has equal charge for any value of its capacitance.

Step-by-Step Explanation:

1. Understanding Series Combination:
When capacitors are connected in series, they are joined end-to-end such that the same electric current flows through each capacitor during the charging process. Since electric current is the rate of flow of charge, the charge flowing into one plate of a capacitor must be equal to the charge leaving the opposite plate and entering the next capacitor in the line.

2. Charge Distribution by Induction:
Let us consider a battery connected across a series combination of capacitors. The positive terminal of the battery draws electrons from the left plate of the first capacitor, leaving it with a charge of:
$$+Q$$
This positive charge induces an equal and opposite charge of:
$$-Q$$
on the right plate of the first capacitor. Since the right plate of the first capacitor is connected to the left plate of the second capacitor (and this segment is isolated from the battery), a charge of:
$$+Q$$
is repelled and deposited onto the left plate of the second capacitor. This electrostatic induction process continues sequentially throughout the entire series chain, regardless of the individual capacitance values.

3. Independence of Capacitance:
The capacitance of a capacitor:
$$C$$
determines the potential difference:
$$V$$
across its plates for a given charge, according to the relation:
$$V=\frac{Q}{C}$$
While the voltage across each capacitor varies depending on its capacitance value, the physical mechanism of charge flow and induction guarantees that the magnitude of charge:
$$Q$$
stored on each capacitor is strictly equal for any value of its capacitance.