Hawkins Electrical Guide v. 01 (of 10) / Questions, Answers, & Illustrations, A progressive course of study for engineers, electricians, students and those desiring to acquire a working knowledge of electricity and its applications

by N. Hawkins

and the joint resistance is equal to the reciprocal[7] of ³⁄₂₀

or 6²⁄₃

In most cases the resistance of the different branches will be alike. This simplifies the calculations considerably. Take, for instance, two branches of 100 ohms resistance each and find the joint resistance.

SOLUTION: ¹⁄₁₀₀ + ¹⁄₁₀₀ = ²⁄₁₀₀; the reciprocal is ¹⁰⁰⁄₂ = 50 ohms, or, in other words, the joint resistance is one-half of the resistance of a single branch, and each branch, of course, will carry one-half of the total current in amperes.

With three branches of equal resistance, the joint resistance will be ¹⁄₃; with four branches ¹⁄₄; with 100 branches ¹⁄₁₀₀ of the resistance of a single branch.

If, for instance, the resistance of an incandescent lamp hot be 180 ohms, the joint resistance of 100 such lamps connected in multiple is

¹⁸⁰⁄₁₀₀ = 1.8 ohms.

If the electromotive force of the system is to be, say 110 volts, then, according to Ohm’s law, the current for 100 lamps is: