Four identical capacitors are joined in series, across a battery of...

Let the capacitance of each capacitor be $C$.

When four identical capacitors are connected in series across a $20\ \text{V}$ battery, the potential difference divides equally among them.

The potential difference across each capacitor is:

$V' = \dfrac{20}{4} = 5\ \text{V}$

The charge acquired by each capacitor is $q = CV' = 5C$.

When these capacitors are separated and connected in parallel (with plates of the same polarity connected together), the total charge of the system becomes:

$Q_{total} = 4q = 4(5C) = 20C$

The equivalent capacitance of the parallel combination is:

$C_{eq} = 4C$

The common potential difference across the parallel combination is:

$V_{common} = \dfrac{Q_{total}}{C_{eq}} = \dfrac{20C}{4C} = 5\ \text{V}$

Answer: $5\ \text{V}$