The potential difference betwee11 the terminals of a cell in an open circuit is 2.2 V. When a resistor of `5 Omega` is connected across the terminals of the cell, the potential difference between the terminals of the cell is found to be 1.8 V. The internal resistance of the cell is

Options

A. `(7)/(12) Omega`
B. `(10)/(9) Omega`
C. `(9)/(10) Omega`
D. `(12)/(7) Omega`

Explanation

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

### Step 1: Identify the given values
- Open circuit potential difference (emf, \( E \)) = 2.2 V
- Potential difference across the terminals when a resistor is connected (\( V \)) = 1.8 V
- Resistance of the connected resistor (\( R \)) = 5 Ω

### Step 2: Use Ohm's Law to find the current
When the resistor is connected, the potential difference across it is 1.8 V. We can use Ohm's law to find the current (\( I \)) flowing through the circuit:
\[ I = \frac{V}{R} = \frac{1.8 \, \text{V}}{5 \, \Omega} = 0.36 \, \text{A} \]

### Step 3: Apply Kirchhoff’s Voltage Law (KVL)
According to KVL, the sum of the potential differences in a closed loop is equal to zero. For our circuit:
\[ E - I \cdot R - V = 0 \]
Where:
- \( E \) is the emf of the cell (2.2 V),
- \( I \cdot R \) is the voltage drop across the internal resistance (\( r \)) of the cell,
- \( V \) is the voltage across the external resistor (1.8 V).

Rearranging gives:
\[ E = I \cdot r + V \]

### Step 4: Substitute the known values
Substituting the known values into the equation:
\[ 2.2 \, \text{V} = I \cdot r + 1.8 \, \text{V} \]
\[ 2.2 \, \text{V} - 1.8 \, \text{V} = I \cdot r \]
\[ 0.4 \, \text{V} = I \cdot r \]

### Step 5: Substitute the current value into the equation
Now substitute \( I = 0.36 \, \text{A} \):
\[ 0.4 \, \text{V} = 0.36 \, \text{A} \cdot r \]

### Step 6: Solve for internal resistance (\( r \))
Rearranging the equation gives:
\[ r = \frac{0.4 \, \text{V}}{0.36 \, \text{A}} \approx 1.11 \, \Omega \]

### Final Answer
The internal resistance of the cell is approximately \( 1.11 \, \Omega \).

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