The circuit above contains 5 resistors (r1, r2, ra, rb, rc) with equal resistance r. write an equation for the current i2 in terms of the current i1. ( when entering your answer, use i1 for i1,

e. g.,the answer 0.5*i1 has the correct syntax) i2 =

0.333 i1

Explanation:

from figure

iB = i2

i1 = iA

i1 = iA = iB+iC = i2+iC

all resistances are equal o R

i1 = E/[R + 2R||R + R] = E/[8R/3] = 3E/8R

since if v is constant then i is inversely proportional to R

iB/iC = R/2R = 1/2

iC = 2iB = 2i2

and i1 = iB+iC = iB+2iB => i1 = 3iB = 3i2

thus i2 = i1/3

or

the equivalent resistance is  

Req = [R || (R+R) ] + ( R + R)

Req = 2R/3 + 2R = 8R/3 ohm

current i1 = E / Req = E / ( 8R/3) = 3E/8R

i1 is divided in two parts as i2 = ib and ic

i1 is divided in i2 and ic in ratio 1 :2

Twice the current will flow through RC as will flow through RB and R2. So the current flowing in R1 and RA is divided by 3,

so i2 is 0.33*i1

i2 = [ 1 / (1+2) ] * i1 = 1/3 * i1    

i2 = i1 / 3 = 0.333 i1