2. How many cells connected in series, each having an EMF of 1.5 V
and internal resistance of 0.2 Ω would be required to pass a current of 1.5 A
through a resistance of 40 Ω.
Load current=1.5 amp
load terminal voltage= 40*1.5=60volts.
voltage drop per battery: .2*1.5=.30 volta
60volts=(1.5-.3)n
n= 50 batteries.
yes
To determine the number of cells connected in series, we need to calculate the total EMF and the total internal resistance required to pass a current of 1.5 A through a resistance of 40 Ω.
Let's start by calculating the total internal resistance:
Formula for total internal resistance:
Total internal resistance (R_total) = Number of cells (n) × Internal resistance per cell (r)
Given:
Internal resistance per cell (r) = 0.2 Ω
Substituting the values into the formula:
R_total = n × 0.2
Next, we need to calculate the total EMF:
Formula for total EMF:
Total EMF (E_total) = Number of cells (n) × EMF per cell (E_per_cell)
Given:
EMF per cell (E_per_cell) = 1.5 V
Substituting the values into the formula:
E_total = n × 1.5
We know that the total current passing through the circuit (I_total) can be calculated using Ohm's Law:
Formula for total current:
I_total = E_total / (R_total + R_load)
Given:
Resistance of the load (R_load) = 40 Ω
Total current (I_total) = 1.5 A
Substituting the values into the formula:
1.5 = E_total / (R_total + 40)
We can rearrange this equation to solve for E_total:
E_total = 1.5 × (R_total + 40)
Now we have two equations:
R_total = n × 0.2
E_total = n × 1.5
We can substitute the value of E_total in terms of n into the second equation:
1.5 × (R_total + 40) = n × 1.5
Next, we can substitute the value of R_total in terms of n into the equation:
1.5 × (n × 0.2 + 40) = n × 1.5
Expanding and simplifying the equation:
0.3n + 60 = 1.5n
Further rearranging:
0.3n - 1.5n = -60
Combining like terms:
-1.2n = -60
Dividing both sides by -1.2:
n = 50
Therefore, 50 cells connected in series, each having an EMF of 1.5 V and an internal resistance of 0.2 Ω, would be required to pass a current of 1.5 A through a resistance of 40 Ω.
To find the number of cells required, we need to use the principles of series circuits and calculate the total EMF and total internal resistance. Given that each cell has an EMF of 1.5 V and an internal resistance of 0.2 Ω, we can proceed as follows:
1. Calculate the total EMF (E_total): Since the cells are connected in series, their EMFs add up.
E_total = Number of cells * EMF per cell
E_total = N * 1.5
2. Calculate the total internal resistance (R_internal): Since the cells are connected in series, their internal resistances also add up.
R_internal = Number of cells * Internal resistance per cell
R_internal = N * 0.2
3. Calculate the equivalent resistance of the circuit (R_total): The equivalent resistance is the sum of the resistance of the load (40 Ω) and the total internal resistance.
R_total = R_load + R_internal
R_total = 40 + (N * 0.2)
4. Use Ohm's Law to find the required current (I) in the circuit:
I = E_total / R_total
5. Set the required current (1.5 A) equal to the calculated current (I) and solve for the number of cells (N).
1.5 = (N * 1.5) / [40 + (N * 0.2)]
Simplifying:
1.5 * (40 + 0.2N) = 1.5N
60 + 0.3N = 1.5N
0.3N - 1.5N = -60
-1.2N = -60
N = -60 / -1.2
N = 50
Therefore, 50 cells connected in series, each having an EMF of 1.5 V and an internal resistance of 0.2 Ω, would be required to pass a current of 1.5 A through a resistance of 40 Ω.