Question

Four capacitors of each of capacity $3\mu F$ are connected as shown in the adjoining figure. The ratio of equivalent capacitance between $A$ and $B$ and between $A$ and $C$ will be :

• A. $4:3$
• B. $3:4$
• C. $2:3$
• D. $3:2$

Answer 1

The correct option is A $4:3$

Equivalent capacitance between A and B

One capacitor of $3\mu F$ is parallel to three capacitor each of $3\mu F$which are in series to each other.

Equivalent capacitance of three capacitors

$\frac{1}{C}=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}$

$C=1\mu F$

Now Let equivalent capacitance between A and B be $C_1$.

$C_1=1+3$

$C_1=4\mu F$

Now equivalent capacitance between A and C

Here two capacitors are in series to each other and parallel to another set of two capacitors in series.

Equivalent capacitance of two capacitors in series

$\frac{1}{C}=\frac{1}{3}+\frac{1}{3}$

$C=1.5\Omega$

Let equivalent capacitance between A and C is $C_2$.

$C_2=1.5+1.5$

$C_2=3\mu F$

Ratio of capacitance

$r=\frac{C_1}{C_2}$

$r=\frac{4}{3}$