Question

The resultant capacitance of four capacitors connected in series is ------------ the smallest individual capacitance

a)less than b)greater than c)equals to d) four times

Answer 1

a)less than

Step-by-step explanation:

The resultant capacitance of N capacitors connected in series is given by

`(1)/(C)=(1)/(C_1)+(1)/(C_2)+....+(1)/(C_N)`

In this problem, since we have 4 capacitances in series, the resultant capacitance is

`(1)/(C)=(1)/(C_1)+(1)/(C_2)+(1)/(C_3)+(1)/(C_4)`

Each of the single term on the right-side of the equation is a positive term: this means that the term
`(1)/(C)` will be larger than the individual terms
`(1)/(C_i)`.

Therefore, this means that the reciprocal, C, will be smaller than each of the individual capacitances
`C_i`.

In particular, if the 4 capacitances are identical,

`C_1=C_2=C_3=C_4=C_0`

So the resultant capacitance will be:

`(1)/(C)=4(1)/(C_0)\\\rightarrow C=(C_0)/(4)`

So the correct answer is

a) less than