# Simple Circuit Analysis: Finding i_{x} with Mesh Analysis

• ttiger2k7
In summary, using mesh analysis, we can find i_{x} by setting up equations for each loop and solving for i_{x}. In this problem, we have three loops with clockwise orientations for i_{1} and i_{x} and a counter clockwise orientation for i_{2}. After solving the equations, we get i_{x} = -0.0125 A. The negative answer indicates that the current is flowing in the opposite direction of the assumed orientation, but the magnitude is correct.
ttiger2k7

## Homework Statement

Use mesh analysis to find $$i_{x}$$.

http://img16.imageshack.us/img16/3384/circuitwd7.jpg

Where $$R_{1}$$ = 100 ohms , $$R_{2}$$ = 50, $$R_{3}$$ =100, R_4 = 220, and $$R_{5}$$ = 470. $$V_{s}$$ = 15 V.

## Homework Equations

$$V = iR$$
$$\Sigma V=0$$

## The Attempt at a Solution

First of all, the current orientation of the left ($$i_{1}$$) and middle ($$i_{x}$$) loops are clockwise, and the right ($$i_{2}$$) loop current is counter clockwise.

Step 1) Finding $$i_{1}$$ and $$i_{2}$$

$$i_{1}$$ = 15/100 = .15 A

$$i_{2}$$ = 9/100 = .09 A

Step 2) Mesh Analysis

$$i_{x}*50+(i_{x}+i_{2})*470+(i_{x}-i_{1})*220=0$$

$$i_{x}*50+(i_{x})*470+(.09)(470)+(i_{x})*220+(.15)(220)=0$$

$$740i_{x}+9.3=0$$

$$i_{x} = -.0125 A$$

*******

The only thing that is bothering me is that I am getting an negative answer. Is this the correct answer using mesh analysis? Thank you.

Last edited by a moderator:
I1 is first mesh, I2 second ... (all 3 clockwise)

sum of voltages around a loop = 0

-15 + 100I1 + 220I1 - 220I2 = 0
220I2 - 220I1 + 50I2 +470I2 - 470I3 = 0
470I3 - 470I2 + 100I3 + 9 = 0

simplfy and solve using augmented matrix

I2 = Ix = 0.014371 amps (if numbers are correct)

Last edited:
Thanks, but the problem is asking for a mesh analysis.

ttiger2k7, I re-did the problem using mesh, hope it helps.

## What is a simple circuit?

A simple circuit is an electrical circuit that consists of a power source, a load, and a conductive path. It is the most basic type of circuit and is used to power basic electronic devices.

## What are the components of a simple circuit?

The components of a simple circuit include a power source (such as a battery or power supply), a load (such as a light bulb or resistor), and conductive materials (such as wires) that connect the components together.

## How do you analyze a simple circuit?

To analyze a simple circuit, you can use Ohm's Law, which states that the current (I) in a circuit is equal to the voltage (V) divided by the resistance (R). You can also use Kirchhoff's Laws, which state that the sum of currents entering a junction in a circuit is equal to the sum of currents leaving the junction, and the sum of voltage drops in a closed loop is equal to the sum of voltage sources in that loop.

## What is the purpose of analyzing a simple circuit?

Analyzing a simple circuit allows you to determine the behavior and characteristics of the circuit, such as the amount of current and voltage at different points, and whether the circuit is functioning properly. This information is important for troubleshooting and designing more complex circuits.

## What are some common applications of simple circuit analysis?

Simple circuit analysis is useful in a variety of fields, including electrical engineering, physics, and electronics. It is used to design and troubleshoot electronic devices, such as computers, televisions, and smartphones. It is also used in power grid systems to ensure the safe and efficient distribution of electricity.

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