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A series-parallel combination battery consists of 300 identical cells, each with an internal resistance `0.3 Omega`. It is connected to the external resistance `10 Omega`. Find the number of parallel goups cosisting of equal number of cells connected in series, at which the external resistance generated the higher thermal power. |
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Answer» Let there be m rows of cells and n cells in each row of a battery. Total number of cells, `N = nm or n = N//m` Let `epslion`,r be the mef and internal resistance of each cell and R be the external resistance. Then total internal resistance of all the m rows of cells ` = nr//m`. Total resistance of the whole circuit `= (R + nr//m)` Total emf of all the cells `=n epsilon` Current in the external resistance R will be `I = (n epsilon)/(R + nr//m) = ((N//m)epsilon)/([R + (N//m) r//m]) = (m N epsilon)/(m^(2)R + N r)` Heat generated in resistance R is `H = I^(2)R= ((m N epsilon)/(m^(2)r + Nr))^(2) R` For H to be maximum, `(dH)/(dm) = 0` Differentiating (ii), w.r.t. m and equation to zero, we get `m =sqrt(Nr//R) = sqrt(300 xx 0.3//10) = 3` |
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