Series & Parallel Resistor Calculator
Determines the net equivalent resistance (R_eq) of up to 4 resistors connected either in pure series or pure parallel. Calculates current distribution and conductance.
PARAMETERS(5)
LOAD VERIFIED SCENARIO
ACTIVE COMPUTATION
Equivalent Parallel Resistance
50Ohms (Ω)
2 parallel paths
Conductance (G = Σ 1/R)
0.02Siemens (S)
STEP-BY-STEP MATHEMATICAL DERIVATION
1Calculated branch conductances: 1/R_total = (1/100) + (1/100) = 0.02 S
2Inverted for equivalent resistance: R_eq = 1 / 0.02 = 50 Ω
MATHEMATICAL FORMULA & GOVERNING PRINCIPLES
Series: R_eq = Σ R_i, Parallel: 1/R_eq = Σ (1 / R_i)
In series, resistances add directly. In parallel, the reciprocals of resistance (conductances) add together, meaning the total resistance is always lower than the smallest branch.
FREQUENTLY ASKED QUESTIONS (FAQ)
Why is parallel resistance always smaller than the smallest branch?
Each parallel branch provides an additional conductive path for electrons, reducing overall impedance to current flow.
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