Series vs Parallel Resistance

In series there is only one path, so the same current flows through both resistors; the resistances add (R_T = R₁ + R₂) and the supply voltage divides between them in proportion to their resistance. In parallel each resistor has its own path directly across the supply, so they share the same voltage but the current splits — more current goes through the smaller resistance. Adding a parallel path always lowers the total resistance below the smallest branch, because you have given the current an extra way through (1/R_T = 1/R₁ + 1/R₂).

• Try this: In series, note the same current everywhere and the voltage split between R₁ and R₂.
• Try this: Switch to parallel — the total resistance drops below the smaller resistor and the total current jumps.
• Try this: Make R₁ ≪ R₂ in parallel and watch most of the current take the low-resistance branch.
• Try this: Set R₁ = R₂ in parallel — the total is exactly half of one resistor.