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

AI Thread Summary
To calculate the current through each resistor in the given circuit, first identify the resistors in series and parallel configurations. The equivalent resistance for resistors R2 and R4 in series with R3 is found to be 5.14Ω, while the total resistance including R1 is 17.14Ω. Using Ohm's Law (V=IR), the total current from the battery can be determined. Kirchhoff's rules can then be applied to find the individual currents through each resistor, considering that current divides at junctions based on resistance. The discussion emphasizes the importance of correctly identifying circuit configurations to solve for currents effectively.
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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.

5385574045_109bd0be85.jpg

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

Homework Equations


V=IR
Req= 1/R1+1/Rn
Req= R1+Rn

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.

Rp=5.14\Omega
Rt=17.14\Omega
 
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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?
 

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