Two identical cells each of emf 1.5 V are connected in parallel across a parallel combination of two resistors each of resistance `20Omega` . A voltmeter connected in the circuit measures 1.2 V. The internal resistance of each cell is :

Options

A. `25 Omega`
B. `4 Omega`
C. `5 Omega`
D. `10 Omega`

Answer

To solve the problem, we need to find the internal resistance of each cell given the following information:

- Two identical cells, each with an EMF (Electromotive Force) of 1.5 V, are connected in parallel.
- The cells are connected across a parallel combination of two resistors, each of resistance 20 Ω.
- A voltmeter connected in the circuit measures a voltage of 1.2 V.

### Step-by-Step Solution:

1. **Understanding the Circuit Configuration:**
- We have two cells in parallel, each with an EMF of 1.5 V.
- The two resistors (20 Ω each) are also connected in parallel.
- The reading on the voltmeter is 1.2 V, which indicates the potential difference across the parallel combination of the resistors.

2. **Calculate the Equivalent Resistance of the Resistors:**
- The equivalent resistance \( R_{eq} \) of two resistors in parallel is given by:
\[ R_{eq} = \frac{R_1 \cdot R_2}{R_1 + R_2} = \frac{20 \cdot 20}{20 + 20} = \frac{400}{40} = 10 \, \Omega \]

3. **Determine the Total Current in the Circuit:**
- The total voltage from the cells is 1.5 V. However, the voltmeter reads 1.2 V, which is the voltage across the equivalent resistance.
- Using Ohm's law, the total current \( I \) flowing through the circuit can be calculated as:
\[ I = \frac{V}{R_{eq}} = \frac{1.2 \, V}{10 \, \Omega} = 0.12 \, A \]

4. **Setting Up the Equation for the Total Voltage:**
- The total voltage from the cells must equal the voltage drop across the equivalent resistance and the internal resistance of the cells.
- The total resistance in the circuit is the internal resistance of the two cells in parallel plus the equivalent resistance of the resistors:
\[ R_{total} = R + R_{eq} = R + 10 \, \Omega \]
- The voltage equation can be set up as:
\[ 1.5 \, V = I \cdot (R + 10) \]
- Substituting the value of \( I \):
\[ 1.5 = 0.12 \cdot (R + 10) \]

5. **Solving for Internal Resistance \( R \):**
- Rearranging the equation:
\[ 1.5 = 0.12R + 1.2 \]
- Subtracting 1.2 from both sides:
\[ 0.3 = 0.12R \]
- Dividing both sides by 0.12:
\[ R = \frac{0.3}{0.12} = 2.5 \, \Omega \]

6. **Final Calculation for Internal Resistance:**
- Since there are two cells in parallel, the effective internal resistance \( R_{internal} \) of each cell is:
\[ R_{internal} = 2.5 \, \Omega \]

### Conclusion:
The internal resistance of each cell is **2.5 Ω**.