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**CIRCUIT ANALYSIS AND TECHNIQUES**

Mesh-Current Method

Using the Mesh-Current method, a circuit can be
described in **b-(n-1)** equations.

On the above circuit there are three resistors.
An unknown current passes through each resistor (i.e. three unknown currents in
total have to be estimated).

But on the above circuit there are two meshes
with currents** i**_{a} and **i**_{b}. By applying
Kirchoff's current law =>

Using the above two equations, currents **i**_{a }
and** i**_{b} could be found. Having found the values of these
currents, the unknown circuit currents could now be found.

**Example**

By observing the above figure find:

- i
_{1} and i_{2}
- the power associated with each voltage
source
- the voltage across the 6 ohm resistor

On the above circuit there are **3 essential
nodes** and **5 essential branches**.

Number of equation needed: **b-(n-1)=3
equations**

**Mesh A:**

...............................(11)

**Mesh B:**

........................(12)

**Mesh C**

.........................(13)

from (11)=>

................................(14)

from (13)=>

..........................(15)

substituting (14) and (15)
into (12) =>

i_{a} = 3.04A

i_{c} = -2.35A

Since** i**_{a} is the
current in the 50V source =>

P(40V) = 50 x 3.04 = 152W

Since** i**_{c} is the
current in the 125V source =>

-2.35 x 125 = -293.75W

Note that ** i**_{c} was
defined as flowing into the 125V source, then the source is actually providing
power.

The current in the 6 ohm
resistor is =>

=> voltage drop = 6 x 1.13 =
6.78V