Minimum resistance obtained from two resistors `3Omega ` and `2 Omega ` is

Options

A. `1 Omega `
B. ` 1.2 Omega `
C. ` 5 Omega `
D. ` 2 Omega `

Answer

To find the minimum resistance obtained from two resistors of 3 ohms and 2 ohms, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Resistors**:
We have two resistors:
- R1 = 3 ohms
- R2 = 2 ohms

2. **Understanding Minimum Resistance**:
The minimum resistance is achieved when the resistors are connected in parallel.

3. **Formula for Parallel Resistance**:
The formula for calculating the equivalent resistance (R_min) when resistors are connected in parallel is given by:
\[ \frac{1}{R_{min}} = \frac{1}{R_1} + \frac{1}{R_2} \]

4. **Substituting the Values**:
Substitute R1 and R2 into the formula:
\[ \frac{1}{R_{min}} = \frac{1}{3} + \frac{1}{2} \]

5. **Finding a Common Denominator**:
The common denominator for 3 and 2 is 6. Thus, we rewrite the fractions:
\[ \frac{1}{3} = \frac{2}{6} \quad \text{and} \quad \frac{1}{2} = \frac{3}{6} \]
Therefore,
\[ \frac{1}{R_{min}} = \frac{2}{6} + \frac{3}{6} = \frac{5}{6} \]

6. **Calculating R_min**:
To find R_min, take the reciprocal of \(\frac{5}{6}\):
\[ R_{min} = \frac{6}{5} = 1.2 \, \text{ohms} \]

7. **Conclusion**:
The minimum resistance obtained from the two resistors is 1.2 ohms.

### Final Answer:
The minimum resistance obtained from the two resistors is **1.2 ohms**.

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