What is the expression used when both current and voltage are unknown for total resistance?

The expression that relates total resistance when both current and voltage are unknown, particularly for resistors in parallel, is represented by the formula where the total resistance is the reciprocal of the sum of the reciprocals of individual resistances. This is formulated as 1/R(t) = 1/R(1) + 1/R(2) + 1/R(3).

When resistors are connected in parallel, the total resistance is less than the smallest individual resistance among them, which is why the total is calculated by summing the reciprocals. This mathematical relationship is essential when designing or analyzing circuits where multiple paths for current exist, making it particularly relevant in fire alarm systems that may use parallel arrangements for redundancy and reliability.

While there are equations for resistors in series and other calculations involving voltage and current (such as Ohm's Law, which relates voltage, current, and resistance), these do not apply here as they do not capture the behavior of resistors in parallel.