वर्गाकार प्लेटों वाले एक समान्तर प्लेट संधारित्र को चित्रानुसार चार परावैद्युतों, जिनके परावैद्युतांक `K_(1), K_(2),K_(3), K_(4)` है, से भर दिया जाता है तो प्रभावी परावैद्युतांक K का मान होगा

Options

A. `K=((K_(1)+K_(2))(K_(3)+K_(4)))/(2(K_(1)+K_(2)+K_(3)+K_(4)))`
B. `K=((K_(1)+K_(2))(K_(3)+K_(4)))/((K_(1)+K_(2)+K_(3)+K_(4)))`
C. `K=((K_(1)+K_(4))(K_(2)+K_(3)))/(2(K_(1)+K_(2)+K_(3)+K_(4)))`
D. `K=((K_(1)+K_(3))(K_(2)+K_(4)))/(K_(1)+K_(2)+K_(3)+K_(4))`

Answer

D

Explanation

`C_(13)=(K_(1)in_(0)L(1)/(2))/(d//2)+K_(3)in_(0)(L.(L)/(2))/(d//2)`
`=(K_(1)+K_(3)) (in_(0)L^(2))/(d)`
`C_(eq)=(K_(1)+K_(4))(in_(0)L^(2))/(d)`
`C_(eq)=(C_(13)C_(24))/(C_(13)C_(24))=((K_(1)+K_(3))(K_(2)+K_(4))in_(0)L^(2))/((K_(1)+K_(2)+K_(3)+K_(4))) (in_(0)L^(2))/(d)`
`=(Kin_(0)L^(2))/(d)`
`K=((K_(1)+K_(3))(K_(2)+K_(4)))/((K_(1)+K_(2)+K_(3)+K_(4)))`