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The n rows each containing m cells in series are joined in parallel. Maximum current is taken from this combination across an external resistance of 3Ω resistance. If the total number of cells used are 24 and internal resistance of each cell is 0.5 Ω then
- a)m=8,n=3
- b)m=6,n=4
- c)m=12,n=2
- d)m=2,n=12
Correct answer is option 'C'. Can you explain this answer?
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The n rows each containing m cells in series are joined in parallel. M...
Ohms. The total resistance of each row is 6 ohms. What is the value of n and m?
We can start by using Ohm's Law to find the total current (I) flowing through the parallel combination of rows:
I = V / R_total
where V is the voltage across the external resistance and R_total is the total resistance of the parallel combination. Since each row has a resistance of 6 ohms, the total resistance of n rows in parallel is:
R_total = 6 / n
Substituting this into the equation for current, we get:
I = V / (6/n)
Simplifying this expression, we get:
I = (nV) / 6
Now, we can use the fact that the maximum current is taken when the external resistance is 3 ohms. In this case, the current is:
I_max = V / 3
Setting this equal to the expression we derived above, we get:
V / 3 = (nV) / 6
Simplifying this equation, we get:
n = 2
This means that there are only 2 rows in parallel. To find the number of cells in each row, we can use the fact that the total resistance of each row is 6 ohms. This means that the resistance of each cell is:
R_cell = 6 / m
Since the cells are connected in series within each row, the total resistance of each row is the sum of the resistances of the individual cells:
6 = mR_cell
6 = m(6/m)
6 = 6
This is a trivial equation, which means that any value of m will satisfy it. Therefore, there is no unique answer for the value of m.
We can start by using Ohm's Law to find the total current (I) flowing through the parallel combination of rows:
I = V / R_total
where V is the voltage across the external resistance and R_total is the total resistance of the parallel combination. Since each row has a resistance of 6 ohms, the total resistance of n rows in parallel is:
R_total = 6 / n
Substituting this into the equation for current, we get:
I = V / (6/n)
Simplifying this expression, we get:
I = (nV) / 6
Now, we can use the fact that the maximum current is taken when the external resistance is 3 ohms. In this case, the current is:
I_max = V / 3
Setting this equal to the expression we derived above, we get:
V / 3 = (nV) / 6
Simplifying this equation, we get:
n = 2
This means that there are only 2 rows in parallel. To find the number of cells in each row, we can use the fact that the total resistance of each row is 6 ohms. This means that the resistance of each cell is:
R_cell = 6 / m
Since the cells are connected in series within each row, the total resistance of each row is the sum of the resistances of the individual cells:
6 = mR_cell
6 = m(6/m)
6 = 6
This is a trivial equation, which means that any value of m will satisfy it. Therefore, there is no unique answer for the value of m.
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The n rows each containing m cells in series are joined in parallel. Maximum current is taken from this combination across an external resistance of 3Ωresistance. If the total number of cells used are 24 and internal resistance of each cell is 0.5Ωthena)m=8,n=3b)m=6,n=4c)m=12,n=2d)m=2,n=12Correct answer is option 'C'. Can you explain this answer?
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