We follow through the same five steps to find the gain as we did in the previous example. Since the circuit is the same as in Ex. 21.1, the total impedance and the current in the circuit are the same:
(Make sure that you can show these on your own!) Again, since the circuit is a series circuit, it follows that I = Is for Step 3.
Now, from Step 4 we get that
Solving for the ratio DVout/DVin gives
(Note that we have again used the relation that 1/j = –j in the previous step, so that 1/(jwC) = –j/(wC). )Finally, from Step 5, the gain is given by the ratio of the magnitudes of the numerator and denominator, which are given by
as found previously in Ex. 21.1. The gain is therefore given by
This is the desired answer. (Look at the bright side—just think of what an algebra expert you’re going to be!)