Two resistors of resistance `R_(1)` and `R_(2)` having `R_(1) gt R_(2)` are connected in parallel. For equivalent resistance R, the correct statement is

Options

A. `RgtR_(1)gtR_(2)`
B. `R_(1)ltRltR_(2)`
C. `R_(2)ltRlt(R_(1) + R_(2))`
D. `RltR_(1)`

Answer

To solve the problem of finding the equivalent resistance \( R \) of two resistors \( R_1 \) and \( R_2 \) connected in parallel, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Parallel Resistance Formula**:
When two resistors are connected in parallel, the formula for the equivalent resistance \( R \) is given by:
\[ \frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \]

2. **Rearranging the Formula**:
To find \( R \), we can rearrange the formula:
\[ R = \frac{R_1 \cdot R_2}{R_1 + R_2} \]

3. **Comparing with Individual Resistances**:
Since \( R_1 > R_2 \), we know that both resistors are positive values. Therefore, the equivalent resistance \( R \) must be less than both \( R_1 \) and \( R_2 \). This is a property of resistors in parallel.

4. **Conclusion**:
Thus, we can conclude that:
\[ R < R_1 \quad \text{and} \quad R < R_2 \]
Therefore, the correct statement is that the equivalent resistance \( R \) is less than either of the individual resistances \( R_1 \) or \( R_2 \).

### Final Answer:
The equivalent resistance \( R \) is less than both \( R_1 \) and \( R_2 \).

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