Question

The equivalent capacitance between $\text{A}$ and $\text{B}$ is

• A. $2\mu \text{F}$
• B. $3\mu \text{F}$
• C. $5\mu \text{F}$
• D. $0.5\mu \text{F}$

Answer 1

The correct option is D $0.5\mu \text{F}$

Let the equivalent capacitance of $1^{st}$ branch be $C_{eq}$.

Since the capacitors are in parallel combination,

So, $C_{eq}=1+1=2\mu \text{F}$

From given diagram,

Equivalent capacitance of $1^{st}$ branch = Equivalent capacitance of $3^{rd}$ branch $=2\mu \text{F}.$

Now circuit becomes


Applying the formula for capacitors in series,

$\frac{1}{C_{eq}^{\prime }}=\frac{1}{C_{eq}}+\frac{1}{C_2}+\frac{1}{C_{eq}}=\frac{1}{2}+\frac{1}{1}+\frac{1}{2}=2$

$\Rightarrow C_{eq}^{\prime }=\frac{1}{2}\mu \text{F}=0.5\mu \text{F}$

Hence, option $\left(d\right)$ is correct.