Solve Current Divider Rule for Resistor Currents w/ R & i

[jti3066]

Homework Statement

Three resistors with resistance 4 ohms, 2 ohms, and R are connected in parallel. There is a total current i through the network. Find the current through each resistor in terms of R and i.

Ignore the 4 ohms and 2 ohms for now I just need help with the CDR formula...Thanks

Homework Equations

i_0 = i_1 + i_2 + i_3

V = V_1 + V_2 + V_3

V_n = i_n * R_n

The Attempt at a Solution

Following the current divider rule I came to the "answer":

i_n = i_0(R_total/R_n)

so for example

i_1 = i_0((R_1 + R_2 + R_3)/R_1)

However my example problem states that the answer should be:

i_1 = i_0(R_2/(R_1 + R_2 + R_3))...?

 

[jti3066]

Wait...is this correct?

i_1 = i_0(R_2 + R_3/R_total)

i_2 = i_0(R_3/R_total)

i_3 = i_0(0/R_total) = 0 because there are no resistor to the right of R_3

 

[gneill]

What's the effective resistance of the parallel combination of three resistors? Call them R1, R2, R3.

Since the total current through the parallel group given as i, what's the voltage across all three? And, given the voltage across all three, you are now in a position to calculate the current though each, right?