Question

there are a large number of cells available , each marked (6V, 0.5ohm) to be used to supply current to a device of resistance 0.75ohm, requiring 24A current. how should the cells be arranged , so that power is transmitted to the load using minimum number of cells?

1) 6 rows, each containing 4cells

2) 4 rows, each containing 6 cells

Answer 1

Case 1

6 rows containing 4 cells

Voltage = 6 * 4 = 24 V

Resistance of Cells in 1 row = 0.5 * 4 = 2 Ω

Resistance of Cells in 6 row = 2/6 = 1/3 = 0.333 Ω

Total resistance including load = 0.75 + 0.333 = 1.083 Ω

Current = 24/1.083 = 22.15 A

less than required 24 A

Case 2

4 rows each containing 6 cells

Voltage = 6 * 6 = 36 V

Resistance in a row = 0.5 * 6 = 3 Ω

Resistance in 4 rows = 3/4 = 0.75 Ω

Total Resistance including Load = 0.75 + 0.75 = 1.5 Ω

Current = 36/1.5 = 24 A

24 A was the required current

so case 2  4 rows, each containing 6 cells is right option