Parallel Resistance

Resistors in Parallel

When resistors share the same two nodes, they are in parallel. Current splits among them.

The Formula

1/R_total = 1/R₁ + 1/R₂ + ... + 1/Rₙ

Or equivalently, summing the conductances (G = 1/R):

G_total = G₁ + G₂ + ... + Gₙ
R_total  = 1 / G_total

For Two Resistors

There's a handy shortcut:

R_total = (R₁ · R₂) / (R₁ + R₂)    ("product over sum")

Key Properties

• Same voltage across every parallel resistor
• Currents add to give total current: I_total = I₁ + I₂ + ...
• Total resistance is always less than the smallest individual resistor
• Two equal resistors in parallel → half their value

Examples

Your Task

Implement double parallel_resistance(double *r, int n) that returns the total parallel resistance.