Question

The equivalent capacitance between $A$ and $B$ for the combination of capacitors shown in figure, where all capacitances are in microfarad is

• A. $6.0\mu F$
• B. $4.0\mu F$
• C. $2.0\mu F$
• D. $3.0\mu F$

Answer 1

The correct option is A $6.0\mu F$

Figure (i) and (ii) are the equivalent circuit of the given circuit.

Figure (i) :

Equivalent capacitance between a and b, $C_1=1\parallel 3$ $\mu F$

$\therefore$ $C_1=1+3=4$ $\mu F$

Equivalent capacitance between c and d, $C_2=6\parallel 2$ $\mu F$

$\therefore$ $C_1=6+2=8$ $\mu F$

Figure (ii) :

The capacitance $\frac{1}{C_3}=\frac{1}{4}+\frac{1}{C_1}$

$\therefore$ $\frac{1}{C_3}=\frac{1}{4}+\frac{1}{4}$ $⟹C_3=2$ $\mu F$

Similarly, the capacitance $\frac{1}{C_4}=\frac{1}{8}+\frac{1}{C_2}$

$\therefore$ $\frac{1}{C_4}=\frac{1}{8}+\frac{1}{8}$ $⟹C_4=4$ $\mu F$

Thus equivalent capacitance between A and B $C_{eq}=C_3\parallel C_4$

$⟹$ $C_{eq}=C_3+C_4=2+4=6$ $\mu F$