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Current divider rule

  • Thread starter jti3066
  • Start date
  • #1
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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)).....?
 

Answers and Replies

  • #2
46
0
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
 
  • #3
gneill
Mentor
20,793
2,773
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?
 

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