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n 1 capacitors, each of capacitance C 1 are connected in parallel and are charged by a source of potential difference V and n 2 capacitors, each of capacitance C 2 are connected in series and are charged by a source of potential difference 4 V . If both the combinations have the same total energy, then C 1 = m C 2 n 1 n 2 . What is the value of m ?

Correct answer

16

Step-by-step solution

A parallel combination of n 1 , capacitors each of capacitance C 1 is, C p = n 1 C 1 Total energy stored in parallel combination, U p = 1 2 C p ( V ) 2 = 1 2 n 1 C 1 V 2    … . ( i ) A series combination of n 2 capacitors each of capacitance C 2 are connected to 4 V source. C s = C 2 n 2 Total energy stored in series combination, U s = 1 2 C s ( 4 V ) 2 = 1 2 C 2 n 2 16 V 2       . . . ii According to give 1 2 C 2 p 16 V 2 = 1 2 n 1 C 1 V 2 n probelm, U s = U p From equations, i and i

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