Consider the circuit shown at right, with all ten billion
(10,000,000,000) switches S1 through S10,000,000,000
initially open. Ten billion “switch demons” then
converge on the circuit and perform the following
actions. Switch demon #1 toggles (i.e., closes an open
switch, or opens a closed switch) every switch S1
through S10,000,000,000. Switch demon #2 then toggles
every second switch, i.e., switches S2, S4, S6, S8, etc.
Switch demon #3 then toggles every third switch, i.e.,
switches S3, S6, S9, etc. This continues in analogous
fashion for the remaining switch demons #4 through
#10,000,000,000, after which all the switch demons
leave. Calculate the resulting current I in the circuit in
its final state. Justify your answer and explain your
reasoning in detail.