CapacitanceHard
Question
A series combination of n1 capacitors, each of value C1 is charge by a source of potential difference 4V. When another parallel combination of n2 capacitors, each of value C2 is charged by a source of potential difference V, it has the same (total) energy stored in it, as the first combination has. The value of C2 in terms of C1 is then
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Solution
A series combination of n1 capacitors each of capacitance C1 are connected to 4V source as shown in the figure
Total capacitance of the series combinatopn of the capacitors is
+ ........upto n 1 terms = 
Cs =
.......(i)
Total energy stored in a series combination of the capcitance is
[Using (i)] ...... (ii)
A parallel combination of n2 capacitors each of capacitance C2 are connected to V source as shown in the figure
Total capacitance of the parallel combinatopn of the capacitors is
Cp + C2 + C2 + C2 ...... upto n1 terms = n2C2
CP = n2C2 .....(iii)
Total energy stored in a parallel combination of the capcitance is
[Using (iii)] ...... (iv)
According to the given problem
Us = UP
Substituting the values of Us and UP from the equation (ii) and (iv), we get
or
n2 C2 or, C2 = 
Total capacitance of the series combinatopn of the capacitors is
+ ........upto n 1 terms = Cs =
.......(i)Total energy stored in a series combination of the capcitance is
[Using (i)] ...... (ii)A parallel combination of n2 capacitors each of capacitance C2 are connected to V source as shown in the figure
Total capacitance of the parallel combinatopn of the capacitors is
Cp + C2 + C2 + C2 ...... upto n1 terms = n2C2
CP = n2C2 .....(iii)
Total energy stored in a parallel combination of the capcitance is
[Using (iii)] ...... (iv)According to the given problem
Us = UP
Substituting the values of Us and UP from the equation (ii) and (iv), we get
or
n2 C2 or, C2 = Create a free account to view solution
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