# Finding current through resistor (Kirchhoff’s Laws)

**1. The problem statement, all variables and given/known data**

Consider the circuit shown in the diagram below, for R1 = 5 Ω, R2 = 8 Ω, R3 = 8 Ω, R4 = 8 Ω, and V0 = 8.0 V. Calculate the current through R4.

**2. Relevant equations**

Loop rule: The sum of all potential changes around a closed loop is zero

Junction rule: The currents entering and leaving a junction are equal

V = IR

**3. The attempt at a solution**

I guess I’m kind of lost with where to begin. The examples in class were a little more simplified but I’ll say what my thought process is to solving it.

First I found the equivalent resistance through the whole circuit

1/R4 + 1/R3 = 1/Req_{34}

1/8 + 1/8 = 1/Req_{34}

Req_{34} = 4 Ω

Then that resistance + R2 = the equivalent resistance on the far left loop

4 + 8 = 12 Ω

Once more, to find the equivalent resistance between that and R1, I went

1/12 + 1/R1 = 1/Req

Req for the circuit = 3.53 Ω

Then to find the current through R4, I’ve been using V = IR where V = 8.0 V and Req = 3.53

I = 2.27 A

This is incorrect, I’m just not quite sure how else to approach this problem. Am I on the right track?

Thanks!

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