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

Options

A. 3 in parallel and 4 in series
B. 2 in parallel and 5 in series
C. 4 in paralleI and 3 in series
D. 5 in parallel and 2 in series

Answer

D

Explanation

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 connect 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 B and D. So, equivalent capacitance.
`C_(eq)=(C_(AB).C_(BD))/(C_(AB)+C_(BD))=(6xx2/4)/(6+2/4)=6/13muF`
Similarly,
(b) 2 capacitors are in parallel and 5 capacitors are connect in series i.e.,


So, equivalent capacitance,
`C_(eq)=(4xx2/5)/(4+2/5)=4/11muF`
(c) 4 capacitors are in parallel and 3 capacitors are connect in series i.e.,

So, equivalent capacitance,
`C_(eq)=(8xx2/3)/(8+2/3)=16/26=8/13muF`
(d) 5 capacitors are in parallel and 2 capacitors are connect in series i.e.,

So, equivalent capacitance,
`C_(eq)=(10xx1)/(10+1)=10/11muF`
So, the correct option is (d).