Question

Four identical condensers are connected in parallel and then in series equivalent capacitance in series to that in parallel combination is

• A. 16 : 1
• B. 4 : 1
• C. 1 : 4
• D. 1 : 16

Answer 1

Answer: (D)

1 : 16

Answer 2

Let's denote the capacitance of each individual capacitor as C. Then, the equivalent capacitance in parallel, Cp, is given by:
Cp = 4C
Now, when capacitors are connected in series, the reciprocal of the equivalent capacitance is equal to the sum of the reciprocals of the individual capacitances.
For our case, since we have four identical capacitors connected in series, the equivalent capacitance in series, Cs, is given by:
$\frac {1}{C_s}$ = $\frac {1}{C}$ + $\frac {1}{C}$+ $\frac {1}{C}$ + $\frac {1}{C}$
$\frac {1}{C_s}$ = $\frac {4}{C}$
Taking the reciprocal of both sides, we get:
Cs = $\frac {C}{4}$
Therefore, the ratio of the equivalent capacitance in series to that in the parallel combination is:
$\frac {C_s}{C_p }$= $\frac {\frac {C}{4}}{4C}$

$\frac {C_s}{C_p }$ = $\frac {1}{16}$
The correct answer is (D) 1 : 16.