# Calculating Current Through 8Ω Resistor with 2 Cells: Homework Solution

• asdff529
In summary, two cells with an EMF of 10V and 4Ω internal resistance are connected to an 8Ω resistor. The current through the 8Ω resistor is 1A, as calculated using the current-divider rule. In order to find the total current through the circuit, the current through the 8Ω must be doubled, resulting in a total current of 2A. Alternatively, the circuit can be simplified by connecting two points with the same voltage, resulting in a total current of 1A through the 8Ω resistor.
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## Homework Statement

two cell,with emf=10V,with 4Ωinternal resistance are connected with a 8Ω resistor as shown in the fig.
What is the current through the 8Ω resistor?

V=IR

## The Attempt at a Solution

If i just consider 1 cell but the internal resistance of another cell is remained there.I guess the current will separate at the point which joint the resistor and the cell.
Here is my calculation
Eq resistance=4+1/(1/8+1/4)
Main current=1.5A
Therefore the current passes through the resistor is 1A
Now come back to the problem,there are 2 cells,so i multiply 1 by 2 and get 2A
But the ans is 1A only

Check your current-divider calculation; The bulk of the current should be flowing through the smaller resistance of a parallel pair

gneill said:
Check your current-divider calculation; The bulk of the current should be flowing through the smaller resistance of a parallel pair

so is my concept right?
thanks a lot

Your approach is correct but you didn't finish it. The figure of 1.5A is correct BUT not all of it flows through the 8 Ohm resistor. Some goes through the 8 Ohm and some goes through the 4 Ohm of the "shorted voltage source" that is in parallel with it. Calculate what fraction flows through the 8 Ohm and double that.

or you can cheat and take a different approach. You can connect any two points with the same voltage together without effecting the circuit. So with the aid of one wire you can reduce the circuit to 2 x 4 Ohm in parallel feeding an 8 Ohm = 10 Ohm. 10V/10 Ohms = 1A...but that wouldn't teach you about superposition.

I would like to first clarify that the calculation provided in the attempt at a solution is incorrect. The equivalent resistance of the two cells and the 8Ω resistor in series is not 4Ω, but rather 8Ω. Using Ohm's Law (V=IR), we can determine that the current through the 8Ω resistor is 1A, as stated in the correct answer. This can also be confirmed by using Kirchoff's Laws to calculate the total current in the circuit, which would also be 1A.

Additionally, it is important to note that the internal resistance of the cells will affect the overall current in the circuit. The higher the internal resistance, the lower the current will be. Therefore, it is important to take into account the internal resistance when calculating the current in a circuit.

Furthermore, the statement that "the current will separate at the point which joint the resistor and the cell" is not entirely accurate. The current will flow through the entire circuit, including the internal resistance of the cells, in a series circuit. It is only in a parallel circuit that the current will split at a junction.

In conclusion, to calculate the current through the 8Ω resistor in this circuit, we must take into account the internal resistance of the cells and use the correct equivalent resistance of 8Ω. This will result in a current of 1A, as stated in the correct answer.

## 1. How do I calculate the current through an 8Ω resistor with 2 cells?

To calculate the current through an 8Ω resistor with 2 cells, you can use Ohm's Law: I = V/R. First, calculate the total voltage by adding the voltage of the two cells together. Then, divide the total voltage by the resistance of the resistor (8Ω) to get the current (in amps).

## 2. What units should I use for this calculation?

The units for voltage should be in volts (V) and the units for resistance should be in ohms (Ω). The resulting current will be in amps (A).

## 3. Can you provide an example of this calculation?

Sure! Let's say you have two cells with a voltage of 1.5V each. The total voltage would be 3V. If you have an 8Ω resistor, the calculation would be: I = 3V/8Ω = 0.375A. Therefore, the current through the resistor would be 0.375 amps.

## 4. What if I have more than 2 cells, how would the calculation change?

If you have more than 2 cells, you would still use the same formula: I = V/R. However, you would need to add the voltage of all the cells together to get the total voltage. For example, if you have 3 cells with a voltage of 1.5V each, the total voltage would be 4.5V.

## 5. Is there a maximum number of cells that can be used in this calculation?

No, there is no maximum number of cells that can be used. As long as you have the voltage and resistance values, you can use as many cells as you need in the calculation. Just remember to add all the voltage values together to get the total voltage.

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