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
By BYJU'S Exam Prep
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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