1Rtot

1Rtot refers to the reciprocal of the total resistance in an electrical network, commonly written as 1/Rtot. This quantity is equivalent to the total conductance of the network and is measured in siemens (S). In many circuit analyses, replacing resistance with conductance simplifies algebra, since current can be expressed as I = V × G, where G is conductance.

In parallel resistor networks, 1/Rtot is equal to the sum of the individual conductances: 1/Rtot = Σ(1/Ri). Equivalently, Gtot = ΣGi, where Gi = 1/Ri. The reciprocal relationship means that adding parallel branches increases the overall conductance and reduces the total resistance.

In series circuits, total resistance is Rtot = ΣRi, so 1/Rtot = 1/(ΣRi). This is not simply the sum of the individual conductances; the reciprocal must be taken after summing the series resistances. For mixed networks, one typically reduces the circuit step by step using series and parallel reductions and then considers the final 1/Rtot.

Example: two resistors, 4 Ω and 6 Ω, in parallel have Rtot = (4×6)/(4+6) = 2.4 Ω, so 1/Rtot = 0.4167 S. The sum of the individual conductances is 1/4 + 1/6 = 0.25 + 0.1667 = 0.4167 S, illustrating the equivalence in parallel configurations.

1Rtot and its related concept, conductance, are fundamental in circuit analysis, facilitating calculations in network admittance, signal processing, and electrical design.