By a cell a current of 0.9 A flows through 2 ohm resistor and `0.3 A` through 7 ohm resistor. The internal resistance of the cell is

Explanation

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

### Step 1: Understand the Circuit
We have a cell with an internal resistance \( r \), connected to two resistors: \( R_1 = 2 \, \Omega \) and \( R_2 = 7 \, \Omega \). The current flowing through \( R_1 \) is \( I_1 = 0.9 \, A \) and through \( R_2 \) is \( I_2 = 0.3 \, A \).

### Step 2: Apply Ohm's Law
According to Ohm's law, the voltage across a resistor is given by:
\[ V = I \cdot R \]
For the first resistor:
\[ V_1 = I_1 \cdot R_1 = 0.9 \cdot 2 = 1.8 \, V \]
For the second resistor:
\[ V_2 = I_2 \cdot R_2 = 0.3 \cdot 7 = 2.1 \, V \]

### Step 3: Write the Voltage Equation
The total voltage \( V \) provided by the cell can be expressed in terms of the internal resistance and the resistances:
\[ V = I_1 \cdot R_1 + I_1 \cdot r \quad \text{(for the first case)} \]
\[ V = I_2 \cdot R_2 + I_2 \cdot r \quad \text{(for the second case)} \]

### Step 4: Set Up the Equations
From the first case:
\[ V = 0.9 \cdot 2 + 0.9 \cdot r \quad \Rightarrow \quad V = 1.8 + 0.9r \quad \text{(Equation 1)} \]
From the second case:
\[ V = 0.3 \cdot 7 + 0.3 \cdot r \quad \Rightarrow \quad V = 2.1 + 0.3r \quad \text{(Equation 2)} \]

### Step 5: Equate the Two Voltage Expressions
Since both expressions equal \( V \):
\[ 1.8 + 0.9r = 2.1 + 0.3r \]

### Step 6: Solve for \( r \)
Rearranging the equation gives:
\[ 0.9r - 0.3r = 2.1 - 1.8 \]
\[ 0.6r = 0.3 \]
\[ r = \frac{0.3}{0.6} = 0.5 \, \Omega \]

### Conclusion
The internal resistance of the cell is \( 0.5 \, \Omega \).

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