In parallel combination, the effective resistance (of `R_(1)` and `R_(2)`) is given by

Options

A. `R=(R_(1)R_(2))/(R_(1)+R_(2))`
B. `(1)/(R)=(1)/(R_(1))+(1)/(R_(2))`
C. `R=R_(1)+R_(2)`
D. `R=(1)/(R_(1))+(1)/(R_(2))`

Answer

To find the effective resistance of two resistors \( R_1 \) and \( R_2 \) connected in parallel, we can use the formula for the effective resistance \( R_{eff} \) in a parallel circuit.

### Step-by-Step Solution:

1. **Understand the Parallel Connection**: In a parallel connection, the voltage across each resistor is the same, but the current through each resistor can be different.

2. **Use the Formula for Effective Resistance**: The formula for the effective resistance \( R_{eff} \) of two resistors \( R_1 \) and \( R_2 \) in parallel is given by:
\[ \frac{1}{R_{eff}} = \frac{1}{R_1} + \frac{1}{R_2} \]

3. **Rearranging the Formula**: To find \( R_{eff} \), we can rearrange the formula:
\[ R_{eff} = \frac{1}{\left(\frac{1}{R_1} + \frac{1}{R_2}\right)} \]

4. **Finding a Common Denominator**: To simplify the right-hand side, we can find a common denominator:
\[ \frac{1}{R_{eff}} = \frac{R_2 + R_1}{R_1 R_2} \]

5. **Final Expression for Effective Resistance**: Therefore, the effective resistance \( R_{eff} \) can be expressed as:
\[ R_{eff} = \frac{R_1 R_2}{R_1 + R_2} \]

### Final Answer:
The effective resistance \( R_{eff} \) of resistors \( R_1 \) and \( R_2 \) in parallel is given by:
\[ R_{eff} = \frac{R_1 R_2}{R_1 + R_2} \]