Question

Which of the following combinations of 7 identical capacitors each of 2 µF gives a resultant capacitance of 10/11 µF?

विकल्प

• 3 in parallel and 4 in series

• 2 in parallel and 5 in series

• 4 in parallel and 3 in series

• 5 in parallel and 2 in series

Answer 1

5 in parallel and 2 in series

Explanation:

For n capacitors i.e., C₁, C₂,.......C_n their equivalent capacitance, when connected in

(a) series is given as, `1/"C"_"s" = 1/"C"_1 + 1/"C"_2 + .....` and 

(b) parallel is given as, C_p = C₁ + C₂ + ....

In the given problem, we will check the net capacitance in each option and compare it with the desired capacitance mentioned in it.

(a) 3 capacitors are in parallel and 4 capacitors are connected in series, i.e.,

where, C_AB is the equivalent capacitance of parallel branches between A and B and C_BD is equivalent capacitance of series capacitors between Band D. So, equivalent capacitance.

`"C"_"eq" = ("C"_"AB" * "C"_"BD")/("C"_"AB" + "C"_"BD")`

`= (6 xx 2/4)/(6 + 22/4)`

`= 6/13 mu "F"`

Similarly,

(b) 2 capacitors are in parallel and 5 capacitors are connected in series i.e.,

So, equivalent capacitance,

`"C"_"eq" = (4 xx 2/5)/(4 + 2/5) = 4/11 mu "F"`

(c) 4 capacitors are In parallel and 3 capacitors are connected in series i.e.,

So, equivalent capacitance,

`"C"_"eq" = (8 xx 2/3)/(8 + 2/3) = 16/26 = 8/13 mu "F"`

(d) 5 capacitors are in parallel and 2 capacitors are connect in series i.e.,

So, equivalent capacitance,

`"C"_"eq" = (10 xx 1)/(10 + 1) = 10/11 mu "F"`

So, the correct option is 5 in parallel and 2 in series.