Analog Electronics Lab #2

Section 1: Resistance

Here are my three resistors and their measurements!

1. )Color code:  red, red, orange, gold
   Stated resistance value: 22k
   Tolerance: + or – 5%
   Min/max possible resistance: /
   5% of 22k ohms = 1.1k Ohms
   minimum= 20.9k Ohms
   maximum= 23.1k Ohms
   Actual measured resistance: 21.88k
   
2. )Color code: yellow, purple, orange, gold
   Stated resistance value: 47k
   Tolerance: + or – 5%
   Min/max possible resistance:
   5% of 47k= 2.35k Ohms
   minimum= 44.65k Ohms
   maximum= 49.35k Ohms
   Actual measured resistance: 46.49k
   
3. )Color Code: brown, black, yellow, gold
   Stated resistance value: 100k
   Tolerance: + or – 5%
   Min/max possible resistance:
   5% of 100k ohms= 5k Ohms
   minimum: 95k Ohms
   maximum: 100k Ohms
   Actual measured resistance: 99.2k Ohms

Section 2: Resistors in Series

Values of Resistors Individually (Stated Values):

1. 22k Ohms Resistor (actual measured value= 21.88k ohms)
2. 47k Ohms Resistor (actual measured value= 46.49k ohms)
3. 100k Ohms Resistor (actual measured value= 99.2k ohms)

Values of Resistors Collectively:

Calculated Collective Value: 169k ohms (using actual measured values 167.57k)
Using Stated Values:
22k Ohms + 47k Ohms + 100k Ohms= 169k Ohms
Using Actual Measured Values:
21.88k Ohms + 46.49k Ohms + 99.2k Ohms= 167.57k Ohms

Actual Measured Collective Value: 167.4k Ohms

Schematic:

Section 3: Resistors in Parallel

Values of Resistors Individually (Stated Values)

1. 22k Ohms Resistor (actual measured value= 21.88k Ohms)
2. 47k Ohms Resistor (actual measured value= 46.49k Ohms)
3. 100k Ohms Resistor (actual measured value= 99.2k Ohms)

Schematic:

Total Resistance of the Circuit Using Measured Values (Calculated): 

Using Measured Values:
1 / [(1/R1) + (1/R2) + (1/R3)]
R1:  21.88k Ohms
R2: 46.49k Ohms
R3: 99.2k Ohms

=1/ ([1/21.88) + (1/46.49) + (1/99.2k)]
=1/ (0.04570 + 0.02151 + 0.01008)
=1/ (0.07729)
=12.93817k Ohms

Using Stated Values:
1 / [(1/R1) + (1/R2) + (1/R3)]
R1: 22k Ohms
R2: 47k Ohms
R3: 100k Ohms

=1/[(1/22) + (1/47) + (1/100)]
=1/[(0.04545) + (0.02128) + (0.01)]
= 1/(0.07673)
= 13.03272

Total Resistance of the Circuit (Measured):

Total Resistance of the Circuit (Measured)= 12.85 Ohms

Section 4: Voltage Dividers

Schematic:

Calculated Vout:
V_IN= 9.28V
R1= 46.33k Ohms
R2= 99.0k Ohms

V_OUT= V_IN X R2/ (r1 +R2)
V_OUT= 9.28V X 99.0k Ohms/(46.33k Ohms + 99.0k Ohms)
V_OUT= 9.28V X 99.0k Ohms/(145.33k Ohms)
V_OUT= 9.28 V X 0.6812k Ohms
V_OUT= 6.3216 V

Measured Vout:
(I need to redo this measurement!)
Measured Vout= 1.682 V

Section 5: Resistors in Series and Parallel

Values of the Resistors:

1. 21.96K Ohms
2. 99.0K Ohms
3. 46.29K Ohms
4. 46.71k Ohms
5. 21.54k Ohms
6. 99.5K Ohms

Calculated:
R_N = 1/ [(1/R₁) + (1/R₂)…(1/R_N)]
=1/ [1/21.96k Ohms) + (1/99k Ohms) + (1/46.29k Ohms)]
=1/ (0.04553 + 0.010101 + 0.0216094)
= 1/ 0.07723394
= 12.9476756k Ohms

R_N = 1/ [(1/R₁) + (1/R₂)…(1/R_N)]
=1/[(1/46.71k Ohms) + (1/21.54K Ohms)]
=1/ (0.02150869 + 0.04642526)
=1/0.06793395
=14.7201804k Ohms

R6 (resistor in series) = 99.5K Ohms

12.9476756k Ohms + 14.7201804k Ohms + 99.5K Ohms
= 127.167856k Ohms

Measured:
=127.5 Ohms

Schematic:

Section 6: Complicated Resistor Networks in Voltage Dividers

Schematic:

Calculated:
V1:
R1= [1 / ((1/R1) + (1/R2)+ (1/R3)]
R1= [1/ (1/21.96k) + (1/99.0k) + (1/46.29k)]
R1= 1/(0.4553 + 0.0101 + 0.02160)
R1= 1/0.487
R1= 2.053388k Ohms

R2= [1 / ((1/R1) + (1/R2)] + 99.5k Ohms
R2= [1/(1/46.71k) + (1/21.54k)] + 99.5k Ohms
R2= 1/[(0.0214) + (0.0464)] + (99.5)
R2= 1/0.0678
R2= 14.7493k + 99.5k
R2= 114.2493 Ohms

V_OUT= V_IN X R2/ (r1 +R2)
V_OUT= 9.28V X 114.2493k Ohms/ (2.053388k Ohms + 114.2493k Ohms)
V_OUT= 9.28V X 114.2493k Ohms/ ( 116.297Ohms)
V_OUT= 9.28V X 0.98234476576
V_OUT= 9.1166V
V1= 9.116

V2:
R1= [1 / ((1/R1) + (1/R2)+ (1/R3)]
R1= [1/ (1/21.96k) + (1/99.0k) + (1/46.29k)]
R1= 1/(0.4553 + 0.0101 + 0.02160)
R1= 1/0.487
R1= 2.053388k Ohms

R1= [1 / ((1/R1) + (1/R2)] + 99.5k Ohms
R1= [1/(1/46.71k) + (1/21.54k)] + 99.5k Ohms
R1= 1/[(0.0214) + (0.0464)] + (99.5)
R1= 1/0.0678
R1= 14.7493k 

R1= 16.80288k Ohms

R2= 99.5k Ohms

V_OUT= V_IN X R2/ (r1 +R2)
V_OUT= 9.28V X 99.5k ohms/ (16.80288k ohms + 99.5k Ohms)
V_OUT= 9.28V X 99.5k Ohms/ (116.30288)
V_OUT= 9.28V X 0.8555
V_OUT= 7.9393
V2= 7.9393V

Measured:
Voltage at Resistor 3: 7.26V
Voltage at Resistor 5: 6.32V

Something is definitely off here!

Section 7: Kirchoff’s Voltage Law

Schematic:

Calculated:
V1:
8.06153V
V1= V_IN X  R2/(R1+R2)
V1= 9.28V X 145.29k ohms/(21.96k Ohms + 145.29k ohms)
V1= 9.28V X 0.86870
V1= 8.06153V

V2:
2.56 V
Vout= Vin X R2/ (r1 +R2)
Vout= 9.28V X 46.29k Ohms/(120.96k Ohms + 46.29k Ohms)
Vout= 9.28V X 46.29k Ohms/(167.25k Ohms)
Vout= 9.28V X 0.2767713
Vout= 2.56843767 V

V3: (???)
V3= V_IN X R2/(R1+R2)
V3= 9.28V X 120.96/(46.29k Ohms + 120.96K ohms)
V3= 9.28V X 120.96/ (167.25 Ohms)
V3= 9.28V X 0.7232
V3= 6.71156V

(I really don’t know what’s happening here)

Measured:
V1: 5.4735V
V2: 2.56V
V3: 1.216V

Analog Troubleshooting Notes Week #2:

Made so many mistakes this week. Click here to check them out!