# Kirchhoff Voltage Law

Lab #10

Kirchhoff’s Voltage

ECET 201-003

ABSTRACT

Kirchhoff's Voltage Law states that the algebraic sum of voltages around a closed path is equal to zero. With regard to the equation it is:

• Vs - V1 - V2 - V3 - V4 = 0

or

• Vs = V1 + V2 + V3 + V4

These equations are essential for understanding the concept of measuring the voltages, it should be possible to verify this relationship. In performing an experiment of this nature, it should be remembered that each measurement is subject to some error. Thus, inconsistencies are expected within the calculations vs the data received from the digital multimeter.

INTRODUCTION

The general principle for series circuits stating that individual voltage drops add up to the total applied voltage, but measuring voltage drops in this manner reveals another facet of this principle: that the voltages measured as such all add up to zero. It doesn’t matter which point we start at or which direction we proceed in tracing the loop; the voltage sum will still equal zero. Kirchhoff’s Voltage Law, denoted as KVL for short, will work for any circuit configuration at all-  simple or complex, series or parallel.

Objective

To Verify Kirchhoff’s Voltage Law for DC circuits.

MATERIALS

1. DC Power Supply 0-10V
2. Digital Multimeter
3. Resistors (+ or - 5%): 1.2k𝛀, 4.7k𝛀, 3.3k𝛀, 6.8k𝛀.

PROCEDURE

1. Select four resistors from the eight available, measure their individual resistance, and record in Table 10-1.
2. Connect the resistors in series, as shown in Figure 10-1.
3. Using the measured values of resistance, calculate and record the total resistance RT and the current I that would result from a source voltage of 10V.
4. Use the calculated current and measured resistance values to predict the voltage drops across each of the resistors record these in the Calculated Voltages row on Table 10-1.
5. Add the calculated values, and record this under the Vsum heading in the Calculated Voltages row. They should sum to 10V.
6. Connect the circuit, and adjust the source to a value of 10V.
7. Measure the voltage across each resistor, and record these in the Measured Voltages row in Table 10-1.
8. Add the measured voltages from step 7 and enter their sum in the appropriate area of the table.
9. Repeat steps 1 through 8 with a different resistor combination, and record all corresponding results in Table 10-2.

RESULTS

Table 10-1 (Vs = 10 V)

 R1 R2 R3 R4 Rt Calculated I (mA) = 0.625 Measured Resistance values (k-ohms) 1.2 3.3 4.7 6.8 16.0 Calculated Voltages V1 V2 V3 V4 Vsum 0.75 2.0625 2.9375 4.25 10.0 Measured Voltages V1 V2 V3 V4 Vsum 0.763 2.117 2.998 4.310 10.20

Table 10-2 (Vs=10V)

 R1 R2 R3 R4 Rt Calculated I (mA) = 0.529 Measured Resistance Values (k-ohms) 2.0 2.2 4.7 10.0 18.9 Calculated Voltages V1 V2 V3 V4 Vsum 1.058 1.1638 2.4863 5.29 9.9981 Measured Voltages V1 V2 V3 V4 Vsum 0.57 1.25 2.69 5.68 10.19 Calculations for Table 10-1: Calculated I:

I= Vs(Rt) = 10V/(1.2 + 3.3 +4.7 + 6.8 k-ohms) =  0.625 mA

Calculated Voltages: Vx=I x Rx

V1= 0.625 mA x R1 = 0.625 mA x 1.2 k-ohms = 0.75 V

V2 = 0.625 mA x 3.3 k-ohms = 2.0625 V

V3 = 0.625 mA x 4.7 k-ohms = 2.9375 V

V4 = 0.625 mA x 6.8 k-ohms = 4.25 V

Vsum = 0.75 + 2.0625 + 2.9375 + 4.25 = 10.2 V

Vsource = 10V, Vsum very close to Vsource

Calculations for Table 10-2:

I= Vs(Rt) = 10V/(2.0 + 2.2 +4.7 + 10.0 k-ohms) =  0.529 mA

Calculated Voltages: Vx=I x Rx

V1= 0.529 mA x R1 = 0.529 mA x 2.0 k-ohms = 1.058 V

V2 = 0.529 mA x 2.2 k-ohms = 1.1638 V

V3 = 0.529 mA x 4.7 k-ohms = 2.4863 V

V4 = 0.529 mA x 10.0 k-ohms = 5.29 V

Vsum = 0.75 + 2.0625 + 2.9375 + 4.25 = 9.9981 V

Vsource=10V, Vsum very close to Vsource again.

Differences due to rubber on the circuit’s wires.

Discussion Questions:

1. Suppose in this experiment, R1=1.8 k-ohms, R2=3.3 k-ohms, R3=4.7 k-ohms, R4=8.2 k-ohms, and Vs=10 V. Voltage V1 should be close to: 10=I/Rt, 10/(18k-ohms) = 555 micro--amps. 555 micro amps x 1.8 k-ohms = 1 V
2. Suppose the conditions are as in question 1, and the following measurements are takien: V1=0.97 V, V2=1.77 V, and V3=2.65 V. Then V4 should be close to: 555 micro amps x 8.2 k-ohms =55 V
3. Continuing with question 2, what is the current? 55 mA
4. If R1, R2, and R3 were all exactly nominal in value and R4 was larger than nominal, then: V4 will be larger than nominal, the other voltages will be smaller than nominal.
5. Explain the effect on total current and each voltage if a single resistor is smaller than its nominal value. The total current will increase since current and resistance are inversely proportional, as told by ohm’s law. Each voltage will remain the same except that single resistor. That resistor will have a smaller voltage.
6. Is it possible to have some voltages less than nominal and some voltages greater than nominal simultaneously in such a circuit? If so, how? I believe it is possible to do so. To do this, one must gather resistors above nominal, and below nominal, in order to balance out the different voltages so they all add up to the source voltage, as is Kirchoff’s voltage law.

CONCLUSION

Overall, this lab helped the group understand that there is a certain amount of error when it comes to calculating the values of the voltages due to certain resistances. Furthermore, it also helped the group understand the difference between a circuit board in parallel and in series. It has also helped the group involve Ohm’s Law with regard to the equations and how they would be applied in a scenario where the error of calculated voltage and actual voltage is involved.

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