Nodal Analysis

Purpose

The purpose of this lab to analyze a circuit with nodal analysis since the given circuit combines elements in series or parallel. Therefore, choosing a node and identifying a ground are important steps before solving the circuit.

Given Problem

Figure 1. 

We can write down equation on V2 and V3 as following

(V1-V2)/100=V2/1000+(V2-V3)/220------->1

(V2-V3)/220+(V4-V3)/220=V3/1000------->2

Solve for equation 1&2 we can get V2=10.26V and V3=8.67V

Ibat1=(V1-V2)/100=0.0174A

Ibat2=(V4-V3)/220=0.0015A

Pbat1=-0.0174*12=-0.2088W

Pbat2=-0.0015*9=-0.0135W

Next we build the circuit up 

Figure 2. 

Connect it with two voltage supplies, and measure the battery current

Figure 3.

The results come out as following

Variable    Theoretical Value     Measured Value         Percent Error 

Ibat1         17.4  mA                 17.12  mA                  1.61 %

Ibat2         1.5    mA                 1.77   mA                    18  %

V2            10.26  V                  10.34  V                     0.78 %

V3            8.67  V                    8.77    V                    1.15 %

Next, we design that we want V2=V3=9V, we need to solve the desired battery voltages

Set the equations up

(V1-9)/100=9/1000+9/220======>V1=9.9 V

(V4-9)/220=9/1000======>V2=10.98 V

We implement the new battery voltage in the circuit and measure the new current again

V2=8.92 V, V3=8.80 , I bat1 = 9.29 mA, I bat2 = 8.03 mA

P.S. This guy allows us to adjust our voltage we want in a range between 0V to 20 V