CBSE Class 12-science Answered
Equivalent capacitance between a and b
Asked by prakriti12oct | 20 Aug, 2019, 01:42: AM
Expert Answer
Let us apply a potential difference V between A and B.
Let q1 , q2 , q3 and q4 are charges on capacitor plates as shown in figure .
Let us apply Kirchoff's Volatge law in the loop, Battery-a-b-c-Battery,
V - (q4 / 2α ) = 0 or q4 = 2V ' .....................(1)
where α = 10-6 μf and V ' = αV
Let us apply Kirchoff's Volatge law in the loop, Battery-a-d-c-Battery,
V - (q1 / 2α ) - (q2 /12α) = 0 or q2 + 6 q1 = 12V ' .....................(2)
By charge conservation at isolated node d,
q1 + q3 = q2 ............................(3)
Let us apply Kirchoff's Volatge law in the loop, d-c-b-d ,
( q2/12α ) - (q4/2α) + (q3/2α) = 0 or q2 = 6 q4 - 6q3 .....................(4)
By solving eqns.(1), (2), (3) and (4),
we get q1 = (3/2)V ' , q2 = 3V ' , q3 = (3/2 )V ' and q4 = 2V '
Total charge Q drawn from battery is given by,
Q = q1 + q3 +q4 = (3/2)V ' + (3/2)V '+2V ' = 5V '
Hence equivalent capacitance, C = Q/V = (5V ' )/V = 5α = 5 μf
Answered by Thiyagarajan K | 20 Aug, 2019, 11:45: AM
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