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CBSE Class 12-science Answered

Two capacitors of unknown capacitance C1 C2 are connected first inseries and then in parallel acrooss a battery OF 100V.If the enenrgy stored in the two combination is 0.145J AND 0.25 J respectively determine thye value of C1 AND C2 .Also calculate the charge on each capacitance in parallel comboination?
Asked by vasturushi | 31 Dec, 2017, 08:57: PM
answered-by-expert Expert Answer
I am facing problem with the numbers given in this question. I feel the energy stored in capacitors connected parallel should be more instead of 0.25J. If i use this value it is not possible to solve. I assume the energy stored in capacitors connected in parallel is 0.75 Joules and show how to solve this problem.
 
Let Cs be the equivlaent capacitance when two capacitors are connected in series.
 
Energy stored in Cs when connected to 100V battery is (1/2)Cs×V2  = (1/2)Cs×100×100 = 0.145 J
 
hence Cs = 29 μF 
 
Let Cp be the capacitance when capacitors are connected in parallel.
 
Energy stored in Cp when connected to 100V battery is (1/2)Cp×V2  = (1/2)Cp×100×100 = 0.75 J
 
hence Cp = 150 μF
 
capacitors connected in series is given by

begin mathsize 12px style C subscript S equals space fraction numerator C subscript 1 C subscript 2 over denominator C subscript 1 plus C subscript 2 end fraction space equals space 29 mu F h e n c e space C subscript 1 C subscript 2 space equals space 29 cross times 150 space p F space open square brackets because space space C subscript 1 plus C subscript 2 space equals space 150 space mu F space close square brackets open parentheses C subscript 1 minus C subscript 2 close parentheses squared space equals space open parentheses C subscript 1 plus C subscript 2 close parentheses squared minus 4 C subscript 1 C subscript 2 space equals space 150 cross times 150 cross times 10 to the power of negative 12 end exponent space minus space 4 cross times 29 cross times 150 cross times 10 to the power of negative 12 end exponent s o l v i n g space f o r space C subscript 1 minus C subscript 2 space g i v e s comma space C subscript 1 minus C subscript 2 space equals space 71.41 cross times 10 to the power of negative 6 end exponent B y space k n o w i n g space C subscript 1 plus C subscript 2 space a n d space C subscript 1 minus C subscript 2 comma space w e space c a n space s o l v e space f o r space C subscript 1 space a n d space C subscript 2 C subscript 1 space equals space 110.7 space mu F space a n d space C subscript 2 equals space 39.3 space mu F space end style

Answered by | 01 Jan, 2018, 04:24: PM

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