Question

The effective capacitance between the point $P$ and $Q$ of the arrangement shown in the figure is:

• A. $\frac{1}{2}\mu F$
• B. $1\mu F$
• C. $2\mu F$
• D. $1.33\mu F$

Answer 1

The correct option is B $1\mu F$

The given circuit can be made like above figure.

This forms a Wheatstone bridge so the capacitor of $5\mu F$gets removed. (fig.1)

Capacitors on the upper branch is in series so their equivalent is (fig.2)

$\frac{1}{C_{eq}}=\frac{1}{2}+\frac{1}{2}$

$C_{eq}=1\mu F$

Similarly, for the lower branch equivalent is $C_{eq}=1\mu F$ (fig.2)

Capacitors $1\mu F$ and $1\mu F$ are in parallel. So equivalent is $2\mu F$ (fig.3)

Now, $2\mu F$ and $2\mu F$ are in series.

So,

$\frac{1}{C_{eq}}=\frac{1}{2}+\frac{1}{2}$

$C_{eq}=1\mu F$