The effective capacitance between points x and y of figure shown is: [AIPMT 1999] |
A) \[6\,\mu F\]
B) \[12\,\mu F\]
C) \[18\,\mu F\]
D) \[24\,\mu F\]
Correct Answer: A
Solution :
[a] The given circuit can be redrawn as |
It is a balanced Wheatstones bridge |
\[\left( as\frac{{{C}_{AB}}}{{{C}_{BD}}}=\frac{{{C}_{AC}}}{{{C}_{CD}}}==\frac{6}{6} \right)\] |
So, potential of B and C are equal and \[20\,\mu F\] capacitor is ineffective. The simplified circuit is shown as: |
Capacitors of \[6\,\mu F\] and \[6\,\mu F\] in upper arms are in series order, so |
\[C'=\frac{6\times 6}{6+6}=\frac{36}{12}=3\,\mu F\] |
Similarly, \[6\,\mu F\] and \[6\,\mu F\] in lower arms are in series order, so |
\[C''=\frac{6\times 6}{6+6}=3\mu F\] |
Now, C and C are in parallel order, hence |
\[C=C'+C''=3+3=6\,\mu F\] |
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