Answer to Question #207180 in Physics for saeed

Question

The Large Electron Positron ring, near Geneva, Switzerland, is one of the biggest scientific instruments on Earth. The circumference of the ring is 27 km. A copper wire with this length and a cross-sectional area of 1 mm2 will have a resistance of about 450 ohms. Consider a parallel connection of three resistors with resistances equal to 1.0, 2.0, and 0.50 times the resistance of the copper wire, respectively, justify by using calculations that the equivalent resistance is 1.3 x 10^2

Answer 1

First, find the values of the resistances:

$$R_1=R, \\ R_2=2R,\\ R_3=0.5R.$$

Next, remember that the equivalent resistance of three resistors connected in parallel is

$$\frac{1}{R_e}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3},\\\space\\ \frac{1}{R_e}=\frac{1}{R}+\frac{1}{2R}+\frac{1}{0.5R},\\\space\\ \frac{1}{R_e}=\frac{1}{R}\bigg(1+\frac12+\frac{1}{0.5}\bigg),\\\space\\ R_e=\frac{R}{3.5}=\frac{450}{3.5}=128.5\Omega.$$