How do you calculate the total resistance in a parallel circuit?

In a parallel circuit, the total resistance is calculated using the formula where the reciprocal of the total resistance is equal to the sum of the reciprocals of each individual resistance. This means that if you have two resistors, R_1 and R_2, in parallel, you find the total resistance by taking the reciprocal of the total resistance, which is equal to adding the reciprocals of R_1 and R_2 together, expressed as 1/R_total = 1/R_1 + 1/R_2.

This relationship arises because, in a parallel circuit, the voltage across each resistor is the same while the current can split between the different paths. By using the reciprocal formula, you account for the increased total current capacity of the circuit when resistors are arranged in parallel. As a result, the total resistance is less than any individual resistance in the parallel arrangement.

The other formulas provided do not apply to parallel circuits: simply adding resistances (as seen in the first choice) pertains to series circuits. The product of resistances (as suggested in the third choice) does not apply in this scenario either. The fourth formula, which suggests that the total resistance is the product of the resistances, is also incorrect for parallel circuits