PhysicsChapter 11: Electricity

Resistors in Parallel

Resistors are in parallel when both ends of every resistor connect to the same two junctions. Each branch therefore has the same potential difference.

Rules to remember

Key equation

V=V₁=V₂=V₃=⋯

Key equation

I=I₁+I₂+I₃+⋯

Key equation

1R_eq=1R₁+1R₂+1R₃+⋯

Voltage is the same across every branch.
Total current equals the sum of branch currents.
Equivalent resistance is smaller than the smallest branch resistance.
For N identical resistors of resistance R, Req=RN.

Useful two-resistor result

Key equation

R_eq=R₁R₂R₁+R₂

Quick solved example

For 6 Ω and 3 Ω in parallel across 12 V:

Key equation

R_eq=(6)(3)6+3=2\ Ω

Key equation

I=122=6\ A

Key equation

I₁=126=2\ A,\qquad I₂=123=4\ A

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