Question

In the given figure, the capacitance $C_1,C_3,C_4,C_5$ have a capacitance $4\mu F$ each. If the capacitor $C_2$ has a capacitance $10\mu F$, then effective capacitance between $A$ and $B$ will be

• A. $2\mu F$
• B. $6\mu F$
• C. $4\mu F$
• D. $8\mu F$

Answer 1

Answer: (C)

Capacitance of capacitors $C_1,C_3,C_4,C_5=4\mu F$ each and capacitance of capacitor $C_4=10\mu F$.
If a battery is applied across $A$ and $B$, the points $b$ and $c$ will be at the same potential (since $C_1=C_4=C_3=C_5=4\mu F$ ).
Therefore no charge flows through $C_2$. We have the capacitors $C_1$ and $C_5$ in series. Therefore their equivalent capacitance,
$C^{\prime }=\frac{C_1\times C_5}{C_1+C_5}=\frac{4\times 4}{4+4}=2\mu F$
Similarly, $C_4$ and $C_3$ are in series.
Therefore their equivalent capacitance,
$C^{\prime \prime }=\frac{C_3\times C_4}{C_3+C_4}=\frac{4\times 4}{4+4}=2\mu F$
Now $C^{\prime }$ and $C$ " are in parallel.
Therefore effective capacitance between $A$ and $B$
$=C^{\prime }+C^{\prime \prime }=2+2=4\mu F.$