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Temple University

College of Engineering

Department of Electrical and Computer Engineering

Lab Report Cover Page

Course Number ECE2113

Course Section 009

Experiment # 2

Name Harsh Patel

TUid# 914139139

Date September 17, 2015

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Lab 1 Part 4 Plotting R = 3.3 kΩ

Procidure 1. Set up the circuit as shown in Figure 3.8 using a 3.3kΩ resister. 2. Measure the resistance use the DDM by setting the DMM to read resistance at a

kilo ohm level. 3. Take the 2 terminals from the DDM and connect the probes at the 2 opposite ends

of the resister to measure the resistance. 4. Set he power supply voltage to 2 volts and read the current displayed on the multi

meter. 5. Repeat steps 4 for all voltage values (VR) on table 3.7 and record your data under

IR 6. Use the Ohm’s law to calculate current in column 3(IR) 7. Use the Formula 3.3 to calculate % Difference 8. Make a current versus voltage graph using the measured IR (DDM) values and

VR values from Table 3.7 9. Once you plot the points draw a best-fit line on the graph and it’s equation. 10. Label the axes and indicate all the data points and name the curve R= 3.3 kΩ. 11. Us this

graph and the trend line to fill out table 3.8 (use current =

0.297(volts)+0) Table 3.7

VR (VOM) IR (DDM) mA IR = VR /Rmeas. mA

%Difference

0V 0 mA 0 mA 0%

2V 0.6 mA 0.59 1.67 %

4V 1.18 1.18 0%

6V 1.78 1.77 0.56 %

8V 2.38 2.36 0.84 %

10 V 2.97 2.96 0.34 %

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IR =2.4 ΔIR =2.4

VR= 0.71 V Δ VR.24V

R= 298Ω R = 300Ω

Table 3.8

In table we found the slope in table 3.6 for 1kΩ and 3.3kΩ resister. When you compare these slops with the actual slopes of the trend line, they match up. You can see from table 8.6 it confirms that the larger the resistance the smaller the slope be cause the slope is the inverse of resistance as we found in table 3.5.

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Introduction

In this lab we will verify the Kirchhoff’s voltage law and its relationship with ohm’s law. The theory is that the (I) in series circuit is same throughout the circuit. The Kirchhoff’s voltage rule says that the total voltage is the sum of voltage from each component of the circuit. We will prove these theories by calculating and measuring the current and the voltage in various circuits. To measure the voltage, we attach DMM (choose DC V mode) in parallel with the component and to measure current we pair the DMM (choose DC I mode) in series with the circuit. Connect the leads properly for each function as instructed on the DDM.

Some Formulas to remember as we do this lab

Ohm’s Law E(V) = I(A) * RT()

Kirchhoff’s voltage law ∑V across branches = 0

Voltage divider V x=V s∗(Rx

RT

) where Vx is voltage through resistor Rx, Vs id the supplied voltage

and the RT is the total resistance.

Part 1 Basic Measurements Procedure

1. Build the circuit as shown on Figure 5.q with R1 being the 220, R2 being 330, and r3 being 470. Measure their resistance individually using the DDM ohmmeter and record the data in table 5.1.

2. Apply12 V from power supply to this series circuit constructed in previous step. Use DMM to measure voltage between each resistors and record the data on table 5.2.

3. Calculate the current through each resistor using the Ohm’s law and record your data on table 5.3

4. Now measure current at point A, B, C and D (refer to Figure 5.2) and record your data on table 5.3

5. Based on data collected in previous step and ohm’s law (V= I*R) fill out table 5.4 for RT in table 5.4. disconnect the power supply and measure the total resistance from point A to D using DMM in resistance mode.

Results and Analysis. Figure 5.1 Figure 5.2

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Table 5.1

Table 5.2

Table 5.3

Based on our voltage readings we can see that Kirchhoff’s voltage law is satisfied. The voltage from power supply was 12 V. If we were to add V1,V2, and V3 out total would turn out to be 11.973 V, which is very close to 12V. This verifies Kirchhoff’s voltage law which states that the total voltage in a loop is zero. Current throughout the series circuit is the same. We also measured the current (I) at the various points in the circuit. Our data on table 5.3 shows that the current is this circuit (figure 5.1) is 11.8 mA, which supports our calculated value in table 5.2.

Resistor #

Ideal resistance

Measured resistance

R1 220 220.0 R2 330 326.3 R3 470 466.5

Voltage (V) Current (mA)

E 12 VV1 2.590 VV2 3.859 VV3 5.529 V

IR1 11.773 mAIR2 11.827 mAIR3 11.841 mA

Current I (mA)A 11.884 mAB 11.884 mA

C 11.884 mAD 11.884 mA

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Part 2 Voltage Divider Rule Procedure

1. Build the circuit as shown on Figure 5.3 with R1 being 100, R2 being 330, and R3

being 680. Measure their resistance individually using the DMM ohmmeter and record the data on table 5.6.

2. Apply 10V to the circuit and measure the voltage (V1, V2, and V3) using an DMM and record data in table 5.6

3. Use the voltage divider rule to calculate V3 and V4 using the measured resistance and record data in table 5.6.

4. Calculate the percent difference between the measured and the calculated values. Use the formula 5.1 and record the percent difference in table 5.6

5. Construct the circuit as shown in figure 5.4 and apply 10V from the power supply to the series circuit. Then measure the voltage through R1 and R2.

ResultsFigure 5.3 Figure 5.4

Formula 5.1 % Diff =|V calc−V meas

V calc|∗100

Table 5.5

Table 5.6

V1 V2 V3 V3 % V4 V4 %

Resistor #

Ideal resistance

Measured resistance

R1 100 100.4 R2 330 326.2R3 680 681.0

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(measured)

(measured) (measured) (Calculated) Difference (Calculated) (measured) Difference

0.889 V 2.938 V 6.512 V 6.148 V 5.927 % 9.094 V 9.091 V 0.0385%We measured the voltage trough each resistor in the circuit (Figure 5.3). If we add up V1,V2, and V3 we would get total voltage in circuit to be 10.034 volts. We applied 10 volts to the circuit and we got 10 volts when we added the voltage through each individual component of the circuit. When we compared our calculated voltage with our measured voltage we got the percent difference of 5.927% it bit high but that is due to our faulty resistor. V4 is the combination of V2 and V3 as we can see in Figure 5.3. The percent difference between V4 calculated and measured is 0.0385%. This is almost the perfect match and this satisfies the Kirchhoff’s voltage law. Based on this data we can also conclude that our desistance measurements for V1 is not very accurate because with V4 (sum of V4 and V3) our percent difference is almost zero. In the second circuit (Figure 5.4) we used some very high resistance values. The voltage across R1 was 20.153 mV and the voltage across R2 was 20.00. This is consistent with the ohm’s law because the voltage is proportional to resistance. The higher the resistance, the higher the voltage.

Part 3 Open Circuit Procedure

1. Build the circuit as shown on Figure 5.6 with R1 being 220, R2 being 1k. Measure their resistance individually using the DMM ohmmeter and record the data on table 5.7.

2. Use the voltage divider rule and calculate V1, V2, and V3 and then apply 16V to the circuit. Using an ohmmeter to measure the voltage at V1, V2, and V3. And record the data on table 5.8.

Results

Figure 4.5 Table 5.7

Table 5.8

Resistor #

Ideal resistance

Measured resistance

R1 220 219.6 R2 1 k 1001.88

Calculated Measured

V1 0 V 0.00 VV2 0 V 0.00 V

V3 16 V 16.00 V

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This circuit was an open circuit but the Kirchhoff law still applies. in table 5.8 we can see that we have zero voltage between V1 and V2 is zero votes, but the difference between V3 was 16v which the supply voltage. This satisfies the Kirchhoff's law and the ohm’s law. Ohm’s law states that the voltage is proportional to resistance relative to the circuit. The resistance between the nodes of V3 is a very high number (for this circuit we will assume its approaching infinity). Based on this theory V3 would have the highest resistance thus having almost all of the voltage supplied by the power supply. Our calculations using the voltage divider rule satisfies our lab data.

Discussion/Conclusion

Through this lab we tested the Kirchhoff’s voltage law and the ohm’s law with various circuits. We measured the current and voltage of various circuits and collected data. We then used this data to back up our calculated values for current and voltage that we calculated using the ohm’s law. in all of our circuits we testes the Kirchhoff’s law applied. The sum of the voltage drop

between each component of the circuit was equivalent to the total voltage supplied to the circuit. In part 3 we verified the voltage divider rule with calculations and the data we collected, satisfies our findings in this lab. This lab helped us become more familiar with basic electronics instruments such as digital millimeter and the DC power supply.