| Property | Series | Parallel |
|---|---|---|
| Equivalent resistance | R_eq = + + … > max(Rᵢ) | 1/R_eq = 1/ + 1/ + … < min(Rᵢ) |
| Current | Same through all (I is constant) | Divides; V = I_{1}$$R_{1} = I_{2}$$R_{2} |
| Voltage | Divides; V = + + … | Same across all (V is constant) |
| If one breaks | All components stop (series failure) | Others continue working |
| Power formula | P = R (use for same-current comparisons) | P = /R (use for same-voltage comparisons) |
| Total power | P_series = ε^{2}/(nR) for n equal R's | P_parallel = nε^{2}/R = × P_series |
| Household use | Not used (different voltages) | Used (each device gets rated V) |
| Capacitor analogy | Series capacitors: 1/C_eq = Σ(1/Cᵢ) — OPPOSITE | Parallel capacitors: C_eq = ΣCᵢ — OPPOSITE |
| For n identical R | R_eq = nR | R_eq = R/n |
Key NEET trap: Series and parallel rules for resistors are OPPOSITE to capacitors. "Resistors and Capacitors are always Rivals."