# To get maximum current through a resistance of 2.5Ω, one can use m rows of cells, each row having n cells. The internal resistance of each cell is 0.5 Ω. What are the values of n and m if the total number of cells is 45? (a). m = 3, n = 15 (b). m = 5, n = 9 (c). m = 9, n = 5 (d). m = 15, n = 3

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Updated on: September 13th, 2023

Given, that the number of rows of cells = m

Number of cells in each row = n

Total number of cells, mn = 45 ————— (1)

The total internal resistance of each cell, r = 0.5 Ω

Total resistance to get maximum current, R = 2.5 Ω

We have to find the values of m and n.

Considering the number of rows in parallel to be m and the number of cells in one row in series be n.

Let us consider each cell has emf E and internal resistance r.

Since there are n cells in each row, equivalent emf, Erow = nE

The internal resistance of each row, row = nr

Since there are m parallel rows of cells, net equivalent emf can be written as

Eeq = ΣnE/nr / Σ1/nr

= mnE/nr / m/nr

= mnE/m

Eeq = nE

Internal resistance, req = nr/m

The current flowing through the circuit can be written as

I = nE / R+(nr/m)

I = mnE / mR+nr

To get maximum current, mR = nr

So, 2.5m = 0.5n

m/n = 0.5/2.5

m/n = 1/5

5m = n ————– (2)

From (1) and (2),

m(5m) = 45

5m2 = 45

m2 = 9

Taking square root, m = ± 3

The value of n cannot be negative, so m = +3

Now, 3(n) = 45

n = 45/3

n = 15

Therefore, the values of m and n are 3 and 15.

Summary:

## To get maximum current through a resistance of 2.5Ω, one can use m rows of cells, each row having n cells. The internal resistance of each cell is 0.5 Ω. What are the values of n and m if the total number of cells is 45? (a). m = 3, n = 15 (b). m = 5, n = 9 (c). m = 9, n = 5 (d). m = 15, n = 3

To get maximum current through a resistance of 2.5Ω, one can use m rows of cells, each row having n cells. The internal resistance of each cell is 0.5 Ω. The values of n and m if the total number of cells is 45 are 3 and 15.

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