Q179 / 180 · COMEDK 2023 (Morning Shift) · Physics
In the figure below, the capacitance of each capacitor is $3 \mu \mathrm{F}$. The effective capacitance between $A$ and $B$ is
- Correct answerA$3 \mu \mathrm{F}$
- B$5 \mu \mathrm{F}$
- C$6 \mu \mathrm{F}$
- D$\dfrac{3}{4} \mu \mathrm{F}$
Solution
Let M be the intermediate node between the two middle capacitors.
Between A and M: top capacitor and left-middle capacitor are in parallel:
$C_{AM} = 3 + 3 = 6\ \mu F$
Between M and B: right-middle capacitor and bottom capacitor are in parallel:
$C_{MB} = 3 + 3 = 6\ \mu F$
$C_{AM}$ and $C_{MB}$ are in series:
$\dfrac{1}{C_{AB}} = \dfrac{1}{6} + \dfrac{1}{6} = \dfrac{2}{6} = \dfrac{1}{3}$
$C_{AB} = 3\ \mu F$
Between A and M: top capacitor and left-middle capacitor are in parallel:
$C_{AM} = 3 + 3 = 6\ \mu F$
Between M and B: right-middle capacitor and bottom capacitor are in parallel:
$C_{MB} = 3 + 3 = 6\ \mu F$
$C_{AM}$ and $C_{MB}$ are in series:
$\dfrac{1}{C_{AB}} = \dfrac{1}{6} + \dfrac{1}{6} = \dfrac{2}{6} = \dfrac{1}{3}$
$C_{AB} = 3\ \mu F$
Hence, the correct answer is option: 'A'.