The potential difference in open circuit for a cell is 2.2 votls . When a `4 ohm`resistor is connected between its two electrodes that potential difference becomes 2 volts. The internal resistance of cell will be

Options

A. `1 ohm`
B. `0.2 ohm`
C. `2.5 ohm`
D. `0.4 ohm`

Explanation

To find the internal resistance of the cell, we will follow these steps:

### Step 1: Identify the Given Values
- Open circuit potential difference (E) = 2.2 volts
- Potential difference when the 4-ohm resistor is connected (V) = 2 volts
- Resistance of the connected resistor (R) = 4 ohms

### Step 2: Apply the Formula for Potential Difference
The relationship between the electromotive force (E), the potential difference (V), the current (I), and the internal resistance (r) of the cell is given by the formula:
\[ V = E - I \cdot r \]

### Step 3: Rearrange the Formula
From the formula, we can express the current (I) in terms of E, V, and r:
\[ I \cdot r = E - V \]
So,
\[ I = \frac{E - V}{r} \]

### Step 4: Calculate the Voltage Drop
Substituting the known values into the equation:
\[ E - V = 2.2 - 2 = 0.2 \text{ volts} \]
This means:
\[ I \cdot r = 0.2 \text{ volts} \]

### Step 5: Express Current in Terms of Resistance
Using Ohm's Law, the current (I) can also be expressed as:
\[ I = \frac{E}{R + r} \]
Where R is the external resistance (4 ohms) and r is the internal resistance we want to find.

### Step 6: Set Up the Equation
Now we can set the two expressions for current equal to each other:
\[ \frac{E}{R + r} = \frac{0.2}{r} \]
Substituting the known values:
\[ \frac{2.2}{4 + r} = \frac{0.2}{r} \]

### Step 7: Cross-Multiply to Solve for r
Cross-multiplying gives:
\[ 2.2r = 0.2(4 + r) \]
Expanding the right side:
\[ 2.2r = 0.8 + 0.2r \]

### Step 8: Rearrange the Equation
Rearranging the equation to isolate r:
\[ 2.2r - 0.2r = 0.8 \]
\[ 2.0r = 0.8 \]

### Step 9: Solve for r
Now, divide both sides by 2.0:
\[ r = \frac{0.8}{2.0} = 0.4 \text{ ohms} \]

### Conclusion
The internal resistance of the cell is:
\[ r = 0.4 \text{ ohms} \]

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