When R1 and R2 are connected in parallel, how is the total resistance calculated?

When R1 and R2 are connected in parallel, how is the total resistance calculated?

• A. (R1 + R2) / (R1 x R2)
• B. (R1 x R2) / (R1 + R2)
• C. R1 + R2
• D. 1 / (R1 + R2)

Answer: (B)

The total resistance for resistors connected in parallel is calculated using the formula: \[ \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} \] This can also be rearranged to give the total resistance in a more straightforward manner, leading to the expression: \[ R_{total} = \frac{R_1 \times R_2}{R_1 + R_2} \] This approach to calculating resistance ensures that the total resistance for parallel resistors—which allows for multiple current paths—will always be less than the smallest individual resistor in the parallel configuration. The correct formula effectively accounts for the distribution of the current between the two resistors, revealing that they work together to allow more flow than either one could alone. The other methods outlined do not represent the correct process for parallel resistance calculations and would yield incorrect total resistance values. Summing the resistances directly, for example, would only apply to resistors in series, not parallel arrangements.

The total resistance for resistors connected in parallel is calculated using the formula:

[ \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} ]

This can also be rearranged to give the total resistance in a more straightforward manner, leading to the expression:

[ R_{total} = \frac{R_1 \times R_2}{R_1 + R_2} ]

This approach to calculating resistance ensures that the total resistance for parallel resistors—which allows for multiple current paths—will always be less than the smallest individual resistor in the parallel configuration. The correct formula effectively accounts for the distribution of the current between the two resistors, revealing that they work together to allow more flow than either one could alone.

The other methods outlined do not represent the correct process for parallel resistance calculations and would yield incorrect total resistance values. Summing the resistances directly, for example, would only apply to resistors in series, not parallel arrangements.