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