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Q.
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
JIPMERJIPMER 2016Electrostatic Potential and Capacitance
Solution:
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,
$C'=\frac{C_{1} \times C_{5}}{C_{1}+C_{5}}=\frac{4 \times 4}{4+4}=2\, \mu F$
Similarly, $C _{4}$ and $C _{3}$ are in series.
Therefore their equivalent capacitance,
$C''=\frac{C_{3} \times C_{4}}{C_{3}+C_{4}}=\frac{4 \times 4}{4+4}=2\, \mu F$
Now $C '$ and $C$ " are in parallel.
Therefore effective capacitance between $A$ and $B$
$= C'+ C ''=2+2=4 \,\mu F .$
