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Question

If 24 cells each of internal resistance I Ω are to be connected in series and parallel combination to get the maximum power output across a load of 10 Ω. If x represents the number of rows and y represents the number of cells in each row. Which of the following relation between x and y is correct?

A
yx=23
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B
yx=10
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C
yx=23
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D
yx=5
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Solution

The correct option is B yx=10

There are x rows and each row has y cells. The total number of cells is x×y=24. Here I=yeR+(yrx)
Maximum power is generated when external load resistance is equal to internal resistance
for maximum power yrx=R or y=10 x or 10 x2=24 or x=2.4=1.55

(I). If x=1, y=24, I=24e34 , where e is the emf of the single cell, then
P1=(24e34)2×10=4.98e2
(I). If x=2, y=12, I=12e16 , where e is the emf of the single cell, then
P1=(12e16)2×10=5.625e2
So we have two rows (x=2) each containing 12 cells (y=12) in series
yx=10

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