- #1

John Wiggum

- 4

- 0

## Homework Statement

The diagram below shows a circuit where; R1 = 5.0 Ω, R2 = 8.0 Ω, R3 = 1.0 Ω, V1 = 16.8 Volts, V2 = 1.5 Volts, and V3 = 39.6 Volts. What is the value of I1? In solving this problem, initially pick the current directions as shown. If the actual current turns out to be in the opposite direction, then your answer will be negative. If you get a negative number, enter it as negative.

Here is a diagram of the circuit with assumed directions of current.\

It should also be noted that my Physics class counts crossing a battery in a KVL loop from its negative terminal to its positive terminal as a positive voltage, and crossing a resistor in a KVL loop in the flow of net positive charge as a negative contribution to voltage for the KVL loop equations.

## Homework Equations

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Kirchoff's Circuit Law: ##Σ I_{in} = Σ I_{out}##

Kirchoff's Voltage Law: ##Σ_{closed~loop} ΔV_i = 0##

Ohm's Law: ##V=I*R##

## The Attempt at a Solution

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So based on the problem picture, and using KCL I determined ##I_1 + I_2 + I_3 = 0## for one of my equations. Then using KVL and drawing two circuit loops shown here I derived two equations. The equation for the 1st loop I found to be ##-I_1*R_1 - V_1 + I_2*R_2 + V_2 = 0##, and I found the equation from the second loop to be ##-I_2*R_2-V_2+I_3*R_3+V_3=0##. When setting up a system of equations and solving them I get ##I_1##=0.5833 amps. This is wrong though and I believe it is a sign error in one of my KVL equations. However, I am unsure of what sign is the issue.