Question

The equivalent capacitance between point A and B is :

• A. 1 $\mu$F
• B. 2$\mu$f
• C. 3$\mu$F
• D. 4$\mu$F

Answer 1

The correct option is D 4$\mu$F

The above diagram can be redrawn as shown in figure.

Now, since capacitor (A), (B), (C), and (D) are in balanced wheatstone condition, so no current will pass through 7$\mu$Fcapacitor so for analysis purpose it can be removed and figure (2) is obtained.

Now, in figure (2), capacitor A and C are in series, while B and D are in series.

So equivalent resistance of capacitor A and C,

$\frac{1}{C_1}=\frac{1}{1}+\frac{1}{2}$

$\Rightarrow C_1=\frac{2}{3}\mu F$

Similarly equivalent resistance of capacitor B and D,

$\frac{1}{C_2}=\frac{1}{2}+\frac{1}{4}$

$\Rightarrow C_2=\frac{4}{3}\mu F$

Now, capacitor $C_1$ , $C_2$ and 2$\mu$F are in parallel

So,

Final equivalent resistance= $\Rightarrow C=\frac{2}{3}+\frac{4}{3}+2=4\mu F$