Question

Net capacitance of three identical capacitors connected in parallel is $12$ microfarad. What will be the net capacitance when two of them are connected in (i) parallel (ii) series?

Answer 1

Hint:The given question has stated that there are three identical capacitors which means all have the same value of capacitance. We have to find the individual capacitance of capacitors. Then we will use the formula of parallel and series combination of capacitance to find the respective solution.

Complete step by step answer:
According to the question all the capacitors are identical. The total capacitance of the circuit when three are connected in parallel combination is $12$ microfarad.

Let the capacitance of each identical capacitor be $C$.
When the capacitors are arranged in parallel combination then we can write,
$\therefore 12 = C + C + C$
$ \Rightarrow 3C = 12$
Solving the equation we get,
$ \Rightarrow C = 4$ microfarad

(i)

Let us find the capacitance of the circuit when two capacitors are in parallel combination.Let the capacitance when two capacitors are connected in parallel be $C'$.We get,
$C' = 4 + 4 = 8$ microfarad

(ii)

Let us find the capacitance of the circuit when two capacitors are in series combination.Let the capacitance when two capacitors are connected in parallel be $C''$.We get,
$\dfrac{1}{{C''}} = \dfrac{1}{4} + \dfrac{1}{4}$
On solving the equation we get,
$ \therefore C'' = 2$ microfarad.

Therefore, when two capacitors are connected in parallel combination then the capacitance is $8$ microfarad and when in series combination gives $2$ microfarad.

Note: It must be noted that the formula of combination of circuit for capacitance is inverse to the combination of circuit for resistance. Capacitance of a circuit implies the energy stored in a capacitor. The parallel combination of a capacitor is just the algebraic sum of the values of each capacitance of a capacitor while the series combination is the sum of reciprocal of the values.