Rtot

Rtot, often written as Rtot or Rtot, denotes the total resistance of an electrical circuit as seen by its terminals. It is measured in ohms and represents the cumulative opposition to current flow provided by all resistive elements and their arrangement within the network.

In series, resistors carry the same current and the total resistance adds: Rtot = R1 + R2 + ... + Rn. In parallel, the resistors share the same voltage and the total resistance obeys 1/Rtot = 1/R1 + 1/R2 + ... + 1/Rn, yielding a value smaller than any individual resistor.

For circuits that mix series and parallel elements, Rtot is found by progressively reducing the network to a single equivalent resistance through valid simplifications or by applying circuit analysis methods such as Kirchhoff's laws or Thevenin/Norton transformations.

In DC circuits, Ohm's law relates Rtot to the total current I and applied voltage V as I = V / Rtot, and the power dissipated is P = V^2 / Rtot or I^2 Rtot. In AC circuits, the total impedance Ztot may be complex; Rtot represents the resistive part, while reactive components contribute to the imaginary part of the impedance.

Examples: two resistors in series, 4 Ω and 8 Ω, give Rtot = 12 Ω. In parallel, 4 Ω and 8 Ω yield Rtot = 1/(1/4 + 1/8) = 8/3 Ω ≈ 2.67 Ω.

Notes: Rtot can depend on temperature or component characteristics for certain resistors, and for nonlinear or variable elements the effective resistance may change with operating conditions. In network analysis, Rtot is typically the Thevenin resistance seen from the circuit’s terminals when independent sources are deactivated.