English
Hindi
2. Electric Potential and Capacitance
medium

એક હવાના મહત્તમ સાથે કેપેસિટર, ડાઈ ઈલેકટ્રીક સાથે કેપેસિટર અને વાહક સ્લેબ સાથે કેપેસિટરની પાસે અનુક્રમે કેપેસિટી $C_1$, $C_2$ અને $C_3$ હોય, તો.....

A

$C_1$ $>$ $C_2$ $>$ $C_3$

B

$C_2$ $>$ $C_3$ $>$ $C_1$

C

$C_3$ $>$ $C_2$ $>$ $C_1$

D

$C_3$ $ >$ $C_1$ $>$ $C_2$

Solution

${C_{1\,}}\, = \,\,\frac{{{ \in _0}\,A}}{d}$

$\,\frac{1}{{{C_2}}}\,\, = \,\,\frac{1}{{2\,{ \in _r}\,{C_1}}}\,\, + \;\,\frac{1}{{2{C_1}}}$

${C_2}\,\, = \,\,\frac{{2\,{ \in _r}\,{C_1}\, \times \,\,2{C_1}}}{{2\,\,{ \in _r}\,{C_1}\,\, + \;\,2{C_1}}}\,\,\,\,\,\therefore \,\,\,\,{C_2}\,\, = \,\,\frac{{4\,{ \in _r}\,{C_1}}}{{2{C_1}\,\,\left( {1\,\, + \,\,{ \in _r}} \right)}}\,\,\, \Rightarrow \,\,{C_2}\,\, = \,\,\frac{{2\,{ \in _r}\,{C_1}}}{{1\,\, + \;\,{ \in _r}}}$

${C_{3\,}}\, = \,\,\frac{{2\,\, \times \,\,\infty {C_1}}}{{1\,\, + \,\,\infty }}\,\, = \,\,\infty $

$\therefore \,\,\,{C_3}\,\, > \,\,{C_2}\,\, > \,\,{C_1}$

Standard 12
Physics

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