Question

10. Four identical condensers each of capacity of 6 microfarads are connected in the form of a
square. Across one of the diagonals of the square, a condenser of capacity 3 microfarad is
connected. The resultant capacity of the combination across that diagonal will be
microfarads
(1 Point​

Answer 1

Given:

4 identical capacitors each of capacity 6 microfarads are connected in the form of a square. Another 3 micro farad capacitor is connected across one of the diagonal.

To find:

Resulting capacitance of a combination considering the terminals to be along the diagonals .

Calculation:

Let the terminals be A and B ;

We can see three parts of the circuit :

• two 6 micro-F capacitor in series

• one 3 micro-F

• two 6 micro-F capacitor in series

The upper part of circuit has net capacitance of C1 :

$C1 = \dfrac{6 \times 6}{6 + 6} = 3 \: \mu F$

The middle part of circuit has net capacitance of C2:

$C2 = 3 \: \mu F$

The lower part of circuit has net capacitance of C3 :

$C3 = \dfrac{6 \times 6}{6 + 6} = 3 \: \mu F$

Now , all these net capacitances are present in parallel combination with one another.

So equivalent Capacitance :

$C \: eq.= (3 + 3 + 3) \: \mu F$

$= > C \: eq.= 9 \: \mu F$

Hence final answer is :

Equivalent Capacitance across AB is 9 micro-F