Mesh Analysis

In this lab mesh current analysis technique will use in order to predict the circuit's physical behavior.

Figure 1: Mesh Current Method

To determine a voltage V1 and V2 is the main

goal of this lab assignment. Three are three

independent DC voltage sources in the circuit.

There are five nodes and three branches.

KVL in the left clockwise loop is (i1):

5 - (10k)i1 - (20k)*(i1+i2) +5 = 0

KVL in the right counterclockwise loop is (i2):

-3 - (6.8k)*(i2) - (20k)*(i2*i1) +5 = 0

These two KVLs make a system equation with two unknown variable i1 and i2.

(30k)*i1 + (20k)*i2 = 10
(20k)*i1 + (26.8k)*i2 = 2

i1 = 0.564 mA , i2 = -0.347 mA

According to Krichhoff's Current Law  (KCL) at node a: I1 = I2 + I3 so I2 = i1 + i2 , I2 = 0.217 mA I1 = i2, I3 = i1

5 - (10k)*(0.564mA) = Va , Va = - 0.64 volts
Va - (20k)*(I2) + 5 = 0 , V2 = (20k)*I2 = Va + 5 = 4.34 v
Va - (6.8k)*I1 + 3 = 0 , V1 = (6.8k)*(I1) = Va + 3 = 2.36 v

Every resistor has a specific tolerance, or a interval accuracy. Resistance of the resistors in the circuit are measured by a DMM.  R1 = 9.81k , R2 = 6.7k , R3 = 22k

According to these resistors (Fig 2) V1 = 2.41 v , V2 = 4.4 v

Percent Error = [(Theory - Measurement) / Theory] * 100%
Percent Error (V1) = [(2.36 - 2.41) / 2.36]*100% = 2.12%
Percent Error (V2) = [(4.34 - 4.4) / 4.34]*100% = 1.38%

Figure 2: Real Resistors and Their measurements

Figure 3: Measure of V2 with a DMM

According to Fig 2, the minimum amount of resistors are R1 = 6.12k , R2 = 18k , R3 = 9k and the maximum amount of the resistors are R1 = 7.48k , R2 = 22k , R3 = 11k.

When minimum or maximum amount of the resistors put in KVL again Va or currents and other parameters do not change.