Find the minimum number of cells connected in two rows in parallel required to pass a current of 6 A through an external resistance of 0.70 ohms. Take the emf of each cell as 2.1 volts and internal resistance of each cell as 0.5 ohm..
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Find the minimum number of cells connected in two rows in parallel required to pass a current of 6A through an external resistance of 0.70 ohms. Take the emf of each cell as 2.1 volts and internal resistance of each cell as 0.5 ohm.
To find the minimum number of cells connected in two rows in parallel required to pass a current of 6 A through an external resistance of 0.70 ohms, we can use Ohm's Law and the concept of total resistance.
1. Start by determining the total resistance of the circuit. Since the two rows are connected in parallel, the total resistance is given by the formula:
1/RTotal = 1/R1 + 1/R2
2. Substitute the given values into the formula. The external resistance is given as 0.70 ohms, so one term in the equation becomes:
1/RTotal = 1/0.70
3. Now, let's calculate the resistance contributed by each cell. Each cell consists of an internal resistance (0.5 ohms) in addition to the external resistance. So, the resistance contributed by one cell is the sum of the external resistance and the internal resistance:
RCell = 0.70 + 0.50
4. Substitute the value of RCell into the equation and calculate it:
1/RTotal = 1/(0.70 + 0.50)
5. Now, solve the equation for RTotal:
RTotal = 1 / (1/(0.70 + 0.50))
6. Calculate RTotal:
RTotal = 1 / (1/1.20)
RTotal = 1.20 ohms
7. Now, since we know the total resistance and the desired current, we can use Ohm's Law to find the total voltage required:
VTotal = ITotal * RTotal = 6 A * 1.20 ohms
VTotal = 7.2 volts
8. Finally, we can determine the number of cells required to achieve this total voltage. The emf of each cell is given as 2.1 volts, so the total emf required is:
ETotal = Number of cells * Emf per cell
7.2 volts = Number of cells * 2.1 volts
9. Solve the equation for the number of cells:
Number of cells = 7.2 volts / 2.1 volts
Number of cells = 3.43
10. Since you cannot have a fractional number of cells, round up to the nearest whole number. Therefore, the minimum number of cells required would be 4.
So, you would need a minimum of 4 cells connected in two rows in parallel to pass a current of 6 A through an external resistance of 0.70 ohms.