Question

Effective capacitance between $A$ and $B$ in the figure shown is (all capacitances are in $\mu F$ )

• A. $ \frac{3}{14}\mu F $
• B. $ \frac{14}{3}\mu F $
• C. $ 21\,\,\mu F $
• D. $ 23\,\,\mu F $

Answer 1

Answer: (B)

The points $C$ and $D$ will be at same potenitals since, $\frac{3}{6}=\frac{4}{8} .$ Therefore, capacitance of $2\, \mu F$ will be unaffected. So, the equivalent circuit can be shown as the effective capacitance in upper arm in series, is given by

$C_{1}=\frac{3 \times 6}{3+6}=\frac{18}{9}=2 \mu F$
The effective capacitance in lower arm in series, is given by
$C_{2}=\frac{4 \times 8}{4+8}=\frac{32}{12}=\frac{8}{3} \mu F$
Hence, the resultant capacitance in parallel is given by
$C=C_{1}+C_{2}=2+\frac{8}{3}=\frac{14}{3} \mu F$