The capacity between the points A and B in the given circuit will be:
A
2C1C2+C3(C1+C2)C1+C2+2C3
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B
C1C2+C2C3+C3C1C1+C2+C3
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C
C1(C2+C3)+C2(C1+C3)C1+C2+3C3
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D
C1C2C3C1C2+C2C3+C3C1
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Solution
The correct option is A2C1C2+C3(C1+C2)C1+C2+2C3 The charge distribution is as shown in the figure. Using Kirchhoff's law, V−q1/C1+(q2−q1)/C3−q1/C1=0⇒V=2q1/C1−(q2−q1)/C3 V−q2/C2+(q1−q2)/C3−q2/C2=0⇒V=2q2/C2−(q1−q2)/C3 Therefore, C1C3V=2C3q1−C2q2+C2q1=(2C3+C1)q1−C1q2 C2C3V=2C3q2−C2q1+C2q2=(2C3+C2)q2−C2q1 Solving these two equations we get,