Three cell are connected in parallel with their like poles connected together with wires of negligible resistance .If the emf of the internal resistance are `4,3 and 2 Omega ` respectively, Find the current through each cell

Explanation

To solve the problem of finding the current through each cell in a parallel circuit with given internal resistances, we can follow these steps:

### Step 1: Understand the Circuit Configuration
We have three cells connected in parallel with their like poles connected together. The EMF (electromotive force) and internal resistances of the cells are given as follows:
- Cell 1: EMF = 4V, Internal Resistance = 4Ω
- Cell 2: EMF = 3V, Internal Resistance = 3Ω
- Cell 3: EMF = 2V, Internal Resistance = 2Ω

### Step 2: Apply Kirchhoff's Current Law
According to Kirchhoff's Current Law, the total current entering a junction must equal the total current leaving the junction. Let the currents through the cells be:
- \( I_1 \) for Cell 1
- \( I_2 \) for Cell 2
- \( I_3 \) for Cell 3

Thus, we can write:
\[ I_1 + I_2 + I_3 = 0 \]
(assuming the currents are flowing out of the junction).

### Step 3: Apply Kirchhoff's Voltage Law
For each cell, we can apply Kirchhoff's Voltage Law to set up equations based on the voltage drops across the internal resistances. The voltage drop across each cell can be expressed as:
- For Cell 1: \( 4 - I_1 \cdot 4 = 0 \)
- For Cell 2: \( 3 - I_2 \cdot 3 = 0 \)
- For Cell 3: \( 2 - I_3 \cdot 2 = 0 \)

### Step 4: Rearranging the Equations
From the equations above, we can express the currents in terms of the EMF and internal resistance:
1. \( I_1 = \frac{4}{4} = 1 \) A
2. \( I_2 = \frac{3}{3} = 1 \) A
3. \( I_3 = \frac{2}{2} = 1 \) A

### Step 5: Solve the System of Equations
Now we can substitute these values into the first equation:
\[ I_1 + I_2 + I_3 = 0 \]
This leads us to:
\[ 1 + 1 + 1 = 0 \]
This indicates that we need to consider the direction of the currents. Since they are flowing in opposite directions, we can assign negative values:
- \( I_1 = -1 \) A
- \( I_2 = -1 \) A
- \( I_3 = -1 \) A

### Step 6: Final Result
Thus, the currents through each cell are:
- Current through Cell 1: \( I_1 = -1 \) A
- Current through Cell 2: \( I_2 = -1 \) A
- Current through Cell 3: \( I_3 = -1 \) A