How Do You Calculate Current Through Each Resistor in Complex Circuits?

[Xels]

Homework Statement

Consider the circuit shown in the figure . Suppose the four resistors in this circuit have the values R₁ = 12 \Omega, R₂ = 6.4 \Omega, R₃ = 7.0 \Omega, and R₄ = 13 \Omega, and that the emf of the battery is \epsilon = 18V .

A. Find the current through each resistor using the rules for series and parallel resistors.
B. Find the current through each resistor using Kirchhoff's rules.

http://www.flickr.com/photos/58789079@N08/5385574045/ by Tetzsc, on Flickr

Homework Equations

V=IR
R_eq= 1/R₁+1/R_n
R_eq= R₁+R_n

The Attempt at a Solution

First I identify R₂ & R₄ as series circuits in parallel with R₃ and solve for the total resistance across these lines giving me 5.14\Omega
I know that I₁-I₂-I₃-I₄ = 0 and that current will take the path of least resistance.
This is where I'm stuck. I know that the current leaving the R₂+R₄ & R₃ will recombine through R₁, but I'm really not sure how to find each individual current.

R_p=5.14\Omega
R_t=17.14\Omega

 

[gneill]

You've calculated the equivalent resistance for the network consisting of R2, R3, and R4. You've also recognized that it's in series with R1. So what's the current that the battery will be providing?