Question

A capacitor with a very large capacitance is in series with a capacitor that has a very small capacitance. what can we say about the capacitance of the series combination? question 1 options:
a.it is slightly smaller than the capacitance of the large capacitor.

b.it is slightly larger than the capacitance of the small capacitor.

c.it is slightly smaller than the capacitance of the small capacitor.

d.it is impossible to say anything about the equivalent series capacitance without knowing the actual numeric values of the individual capacitors in the combination.

e.it is slightly larger than the capacitance of the large capacitor.

Answer 1

A capacitor with a very large capacitance is in series with a capacitor
that has a very small capacitance.

The capacitance of the series combination is slightly smaller than the
capacitance of the small capacitor. (choice-C)

The capacitance of a series combination is

             1 / (1/A + 1/B + 1/C + 1/D + .....) .

If you wisk, fold, knead, and mash that expression for a while,
you find that for only two capacitors in series, (or 2 resistors or
two inductors in parallel), the combination is   

             (product of the 2 individuals) / (sum of the individuals)  .

In this problem, we have a humongous one and a tiny one.
Let's call them  1000  and  1 .
Then the series combination is

           (1000 x 1) / (1000 + 1)

        =       (1000) / (1001)

        =         0.999 000 999 . . . 

which is smaller than the smaller individual.

It'll always be that way.