EE316-Lab1 Resistive Circuits, Linear Scale Ohmmeter Solved

 
Purpose 
The goals of this laboratory are to verify Ohm’s Law, Kirchhoff’s Voltage Law, and Kirchhoff’s Current Law. In addition, the operational ranges for voltages and currents as related to component tolerances will be explored. 

Theoretical Background 

Ohm’s Law 
Ohm’s Law states that the voltage across a linear resistor is directly proportional to the current flowing through the resistor. Mathematically, the voltage, current, and resistance are related by 

V = I*R 

Kirchhoff's Voltage Law (KVL) 
Kirchhoff's Voltage Law states the algebraic sum of the voltages around any closed path or loop in a circuit must be equal to zero. That is for the circuit below: 

Vs = V1 + V2 
  

Figure 1.1 

Kirchhoff’s Current Law (KCL) 
Kirchhoff’s Current Law states that the algebraic sum of the currents entering a node must be equal to the algebraic sum of the currents leaving the node.  

Mathematically: 

I1 = I2 + I3 
  

Figure 1.2 

Theoretical Analysis 
Referring to Figure 1.3, calculate the circuit’s Branch Voltages, Branch Currents, Node Voltages, and Loop Currents with the following assumptions. (Note: Mesh Analysis may be useful here.) 

1.       First assume all the resistors are exact (i.e. a 10 ohm resistor is exactly 10 ohms). 

2.       Then assume all resistors are 10% above the exact values. 

3.       Then assume all resistors are 10% below the exact values. 

Record all your data in tabular format similar to Table 1.1. Let the exact values of source voltage and resistors be defined by the following values: 

Vs = 5.0V 

R1 = R2 = R3 =100 R4 = R5 =1 K R6 = R7 =2.2 K 
  

Figure 1.3 

 

Simulation 
Build the circuit Figure 1.3 using the Electronics Workbench. Then place virtual Volt and Ammeters in the circuit to find all required voltages and currents that you found in the theoretical analysis section. Print out the schematic showing all the readings before moving on to the next section. 

Laboratory Procedure 

Part A 
Using the Analog/Digital trainer, build the circuit and re-measure all Branch Voltages, Branch Currents, Node Voltages, and Loop Currents using a digital multimeter. 

Record all the specified measurements in a table similar to Table 1.1. 

TABLE 1.1 
                                                

Branch Voltages 
Branch Currents 
Node Voltages 
Loop 

Currents 
VR1 = 
iR1 = 
V1 = 
I1 = 
VR2 = 
iR2 = 
V2 = 
I2 = 
VR3 = 
iR3 = 
V3 = 
I3 = 
VR4 = 
iR4 = 
V4 = 
 
VR5 = 
iR5 = 
 
 
VR6 = 
iR6 = 
 
 
VR7 = 
iR7 = 
 
 
 

1.                  Verify each of the following using your experimental results. Account for component tolerances in the calculations if necessary. 

 

a.       Ohm’s Law 

b.       Kirchhoff's Voltage Law 

c.       Kirchhoff's Current Law 

 

2.                  Compare your experimental results for voltages and currents with the results from a theoretical analysis. Do your experimental values fall within operational ranges? Explain in detail. 

 

Part B 
Build the circuit shown in Figure 1.4. 

  

Figure 1.4 

 

Set your source voltage and resistance values as follows; let Vs = 5.0 Volts and Rs = 100 . It does not matter if these values are exact as long as they remain consistent throughout the experiment.

 

1. Measure and record the values of load voltages and currents for various values of RL (load resistance) as specified in Table 1.2. Use a variable resistor to vary the load resistance. 

Table 1.2 
                                                       

 

RL (Ohms) 
 

VL (V) 
 

IL (mA) 
10 
 
 
20 
 
 
40 
 
 
70 
 
 
100 
 
 
150 
 
 
200 
 
 
300 
 
 
500 
 
 
1000   

 

1. Using your data and a spreadsheet program plot VL vs. IL. Determine and report the values of x and y intercepts, and the slope of the line.