C धारिता के संधारित्र `C _1 ` को `V _0 ` विभवान्तर तक आवेशित किया जाता है। इस आवेशित संधारित्र को C/2 धारिता के अनावेशित संधारित्र से जोड़ा जाता है।

Options

A. `{:(,A,B,C,D),((a),1,2,3,5):}`
B. `{:(,A,B,C,D),((b),4,5,3,1):}`
C. `{:(,A,B,C,D),((c ) ,5,4,3,1):}`
D. `{:(,A,B,C,D),((d),1,2,3,4):}`

Answer

B

Explanation

` A to 4, B to 5, C to 3, D to 1 `
` because (Q_1)/(C_1) = (Q_2)/(C_2) .Q_1 = ((C_2)/(C_1)) , Q_1`
` = ((C//2)/( C )) . Q_1 = (Q_1)/(2)`
` Q = Q_1 +Q_2 =Q_1 +(Q_1)/(2) = 3 (Q_1)/(2)`
` Q_1 = (2)/(3) Q ` तथा ` Q_2 = (1)/(3)Q `
`U_1 = (Q_1^(2))/(2C_1) = ((2//3Q)^(2))/(2C)`
` = (2)/(9) ((Q^(2))/(C ) ) =(2)/(9) ((C^(2)V_0^(2))/(C ) ) `
` = (2)/(9) ((Q^(2))/(C)) = (2)/(9) ((C^(2) V_0^(2))/(C )) `
` = (2)/(9) CV_0^(2) " " ( because Q = CV_0 )(A to 4 ) `
` (B to 5) U_2= (Q_2^(2))/(2C_2) = ((1)/(3) Q)^(2)/(2 ((C)/(2)))`
`= (1)/(9) ((Q^(2))/(C)) = (1)/(9) CV_0^(2)`
` (C to 3 ) U_ ("अंतिम ") =U_1 +U_2 = (1)/(3) CV_0^(2)`
` (D to 1 )U_(" prarambhik ") = (Q^(2))/(2C) = ((CV_0)^(2))/(2C) `
`= (1)/(2) CV_0^(2) `
ऊर्जा में परिवर्तन ` ,Delta U=-(1)/(6) CV_0^(2)`