Two cells of emf `E_1=6V` and `E_2=5` are joined in parallel with same polarity on same side without any external load. If their internal resistance are `r_1 =2Omega` and `r_2=3Omega` respectively, then

Options

A. terminal potentiasl difference across any cell is less than `5V`
B. terminal potential differences any cell is `5.6V`
C. current through the cells is `0.2 A`
D. current through the cells is zero if `E_1=E_2`

Explanation

To solve the problem step by step, we will use Kirchhoff's voltage law (KVL) and the concepts of internal resistance in parallel circuits.

### Step 1: Understand the Circuit Configuration
We have two cells connected in parallel:
- Cell 1 with emf \( E_1 = 6V \) and internal resistance \( r_1 = 2 \Omega \)
- Cell 2 with emf \( E_2 = 5V \) and internal resistance \( r_2 = 3 \Omega \)

### Step 2: Apply Kirchhoff's Voltage Law (KVL)
To find the current flowing through the circuit, we can apply KVL to the loop formed by the two cells. We assume a current \( I \) flows through the circuit.

Starting from one point in the loop (let's call it point A) and going around the loop, we can write the KVL equation:
\[ E_1 - I r_1 - E_2 - I r_2 = 0 \]
This simplifies to:
\[ E_1 - E_2 = I (r_1 + r_2) \]

### Step 3: Substitute the Values
Substituting the given values into the equation:
\[ 6V - 5V = I (2 \Omega + 3 \Omega) \]
\[ 1V = I (5 \Omega) \]

### Step 4: Solve for Current \( I \)
Now, we can solve for \( I \):
\[ I = \frac{1V}{5 \Omega} = 0.2 A \]

### Step 5: Calculate Terminal Potential Difference for Cell 1
To find the terminal potential difference across cell 1, we can use the formula:
\[ V_{AB} = E_1 - I r_1 \]
Substituting the values:
\[ V_{AB} = 6V - (0.2 A \times 2 \Omega) = 6V - 0.4V = 5.6V \]

### Step 6: Calculate Terminal Potential Difference for Cell 2
Similarly, for cell 2, we can use:
\[ V_{CD} = E_2 + I r_2 \]
Substituting the values:
\[ V_{CD} = 5V + (0.2 A \times 3 \Omega) = 5V + 0.6V = 5.6V \]

### Summary of Results
- Current flowing through the circuit \( I = 0.2 A \)
- Terminal potential difference across cell 1 \( V_{AB} = 5.6 V \)
- Terminal potential difference across cell 2 \( V_{CD} = 5.6 V \)