Question: If the equivalent capacitance between A and B of the combination of capacitors shown in figure is 3C...

Question

If the equivalent capacitance between A and B of the combination of capacitors shown in figure is 3C, the capacitor C' 'is equal to

Answer 1

Solution

The three 2C capacitors are in parallel, so their equivalent capacitance is 2C + 2C + 2C = 6C. This 6C capacitor is in series with C'. The equivalent capacitance of the series combination is given by:

C_{eq} = \frac{C_1 C_2}{C_1 + C_2}

In this case, $C_1 = 6C$ and $C_2 = C'$ , and we are given that $C_{eq} = 3C$ . Therefore:

3C = \frac{6C \cdot C'}{6C + C'}

Multiplying both sides by $6C + C'$ gives:

3C(6C + C') = 6C \cdot C'

18C^2 + 3CC' = 6CC'

18C^2 = 3CC'

Dividing both sides by $3C$ (since $C \neq 0$ ):

6C = C'

Thus, $C' = 6C$ .