# Find voltage across resistor using mesh current analysis

• vizakenjack
In summary, The conversation discusses finding Vth using mesh current analysis. It is noted that Mesh A and B share a current source and are treated as one supermesh. The equation for this supermesh is given as +12V + ia(6Ω) + ib(6Ω + 4Ω) = 0. It is also mentioned that the loop with the open circuit can be ignored since there is no current flowing through it. The final values for ia and ib are calculated and the voltage across 4Ω (Vth) is found to be 40V instead of the expected 6V. In order to find the correct value, the voltages across all resistors are summed in a
vizakenjack
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I'd like to find Vth by mesh current analysis.

Mesh A and B share a current source, so they're treated as one supermesh.

What's the equation for this supermesh? Also, do I ignore the loop with the open circuit? Since there's no current flowing there...

2A = ib - ia

Anyway, is this the right equation:

+12V + ia(6Ω) + ib(6Ω + 4Ω) = 0?

if yes, then my ia ends up being -32V/(4Ω) = - 8A

ib = 2A + 8A = 10A

And the Voltage across 4Ω (Vth) = ib * 4Ω = 40 V!

But that's not correct, Vth should be 6V!

vizakenjack said:
+12V + ia(6Ω) + ib(6Ω + 4Ω) = 0?
With currents marked clockwise, the voltages across all resistors here sum clockwise as voltage falls, and you could pencil in a small + and - sign on each resistor as a reminder.

So summing in a clockwise path the voltage rises around the loop:
+12 - ia(6) - ib(6+4) = 0

vizakenjack

## 1. What is mesh current analysis?

Mesh current analysis is a method used to find the voltage across a specific resistor in a circuit. It involves assigning current values to different loops or "meshes" in the circuit and using Kirchhoff's Voltage Law (KVL) to solve for the voltage across the desired resistor.

## 2. How does mesh current analysis differ from other circuit analysis methods?

Unlike other analysis methods such as nodal analysis, mesh current analysis focuses on the current flow within specific loops in the circuit rather than the potential difference at specific nodes. This can be especially useful when dealing with circuits that have multiple current sources and multiple loops.

## 3. What are the steps involved in performing mesh current analysis?

The steps for mesh current analysis are as follows: 1. Identify the number of meshes in the circuit 2. Assign current variables (i1, i2, etc.) to each mesh 3. Apply Kirchhoff's Voltage Law (KVL) to each mesh, setting up equations 4. Solve the resulting system of equations for the desired voltage value.

## 4. Can mesh current analysis be used for all types of circuits?

Mesh current analysis can be used for most types of circuits, including those with multiple voltage sources, current sources, and resistors. However, it may become more complex and time-consuming for circuits with a large number of meshes and components.

## 5. What are some advantages of using mesh current analysis?

Some advantages of using mesh current analysis include the ability to handle circuits with multiple current sources and the fact that it can be applied to both planar and non-planar circuits. Additionally, the use of KVL makes it a straightforward and systematic method for solving for the voltage across a specific resistor in a circuit.

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