What formula is used to calculate total resistance in parallel circuits?

The formula for calculating total resistance in parallel circuits is based on the reciprocal of the individual resistances. When resistors are connected in parallel, the total current flowing through the circuit is the sum of the currents through each resistor. Since the voltage across each resistor remains the same, the total resistance can be found using the equation ( \frac{1}{R_{total}} = \frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3} ).

This relationship arises because, in a parallel configuration, each resistor provides an alternate pathway for the current, which effectively decreases the overall resistance of the circuit. Therefore, the reciprocal of the total resistance is equal to the sum of the reciprocals of each individual resistance. This results in a total resistance that is always less than the smallest resistance in the group.

Using this formula allows for accurate calculations of total resistance in circuits where multiple resistive pathways are available, enabling efficient circuit analysis and design.