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CBSE Class 12-science Answered

Equivalent capacitance between a and b 
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Asked by prakriti12oct | 20 Aug, 2019, 01:42: AM
answered-by-expert 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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