9/14/17 Mesh Analysis III

Mesh Analysis |||

Date : 9/14/17

Overview 

Use mesh analysis to analysis a circuit containing multiple sources. Fine I1 and V1

Pre-lab

Calculate I1 and V1. (note : we measured actual resistors and then calculated from new resistor values). 

loop 1: 

           4.4k (i21- i2) + 1k (i1) + 6.4k (i1 - i3)  = 0 

           simplifies to  11.8k (i1) - -4.4k (i2) - 6.4k (i3)  = 0 

loop 2

         4.4k (i2 - i1) + 5 -2 = 0 

        simplifies to    -4.4k (i1) + 4.4 (i2) = -3 

loop 3

         6.4k (i3-i1) + 21k (i3) - 5 = 0 

         simplifies to   -6.4k (i1) + 27.4k (i3) = 5 

matrix of loop1,2,3

 

I1 =  - 3.1026 x 10^(-4) A = -310 μA

I2 =  -9.9208 x 10^(-4) A =  -992 μA

I3 =  1.1 x 10^(-4) A = 110 μA

V1  (V = IR ) 

       V1 = (110μA) (21,000)

       V1  = 2.31 volts

Lab 

1a) Measure and record all actual resistance
        4.7k (resistor) = 4.4k (actual resistor)
        1.5k (resistor) = 1k    (actual resistor)
        6.8k (resistor) = 6.4k (actual resistor)
        20k  (resistor) = 21k  (actual resistor)

1b) Measure V1 and I1 circuirt
          V1 (recorded value) = 2.37 volts

      Percentage error from calculated V1 and recorded V1
           ((2.37-2.31) / (2.31)) * 100 = % 2.6 error

2) Picture of circuit

Comments : Our calculated value of V1  of 2.31 volts matches the simulated value in the Every Circuit App, along with our calculated value of I1 = 310 μA. Our negative calculated values of I0 and I1 designates opposite direction of current flow as indicated in the figure in prelab or in the Every Circuit figure above. 

In each lab, we have use calculated values which at times results in everyone getting different answers until we all agree. Sometimes our recorded values is different than expected where we then try to trouble shoot what the issue is which mainly occurs with a loose wire, wrong resistor, wrong voltage source cable location or simply multi-meter error. Using the Tinker Cad app to display a simulated breadboard version helps to visualize our circuit when it is hard to read in the photo and confirm our calculated values. As shown with Tinker Cad, both I1 and V1 are same as our calculated values. 

TinkerCadApp

EveryCircuitApp