KIRCHHOFF’S RULES

EXPERIMENT 7: KIRCHHOFF’S RULES

INTRODUCTION

• Kirchhoff’s current rule defines the way that electrical current is distributed when it is applied to a junction in a circuit- a point in the circuit where charge has several possible paths to travel.

• Once charge has entered into the junction, it has no place to go except to leave (this is known as conservation of charge). The total charge flowing into a junction must be the same as the the total charge flowing out of the junction.

• Kirchhoff's Laws allows us to analyse more complex circuits, which are not composed exclusively of parallel or series components.

OBJECTIVES

• To verify Kirchhoff's rule.

• To determine the value of currents in each resistor in the circuit.

• To determine the value of potential differences across each resistor in the circuit

1. There are two rules in Kirchhoff’s rules• The Junction Rule• The Loop Rule

2. The junction rule states that the current entering any point in a circuit must equal to the current leaving that point.

3. The loop rule states that the sum of the potential differences across each circuit element in a closed loop must be zero.• To write down a loop equation, you choose a starting

point, and then follow a path around the loop in one direction until you get back to the starting point. As you cross a battery or a resistors note the change in voltage. Add these changes in voltage and set the sum equal to zero

KIRCHHOFF’S RULES

JUNCTION RULE

LOOP RULE

APPARATUS

• Battery or DC power supply• Ammeter• Voltmeter• Three carbon resistors• Connecting wires

PROCEDUREA. Determining the Currents and Potential

Differences for Resistors With a Single Voltage Source

1. The circuit is set up as shown in the figure.

2. The voltage supply from electrical circuit board is measured and the value is 7V.

3. The potential difference across each resistor is measured. The voltmeter must be parallel with the resistor.

4. The current reading for each resistor is measured. The ammeter must be in series with resistor.

B. Determining the Currents and Potential Differences for Resistors

With Two Voltage Sources

1. The circuit is set up as shown in the figure.

2. The potential difference across each resistor is measured.

3. The current reading for each resistor is measured.

RESULT AND ANALYSIS

Resistance, R (Ω ) Current, I (mA) Voltage, V (V)

R₁ 746.44 I₁ 3.51 X 10-3 V₁ 2.62

R₂ 751.07 I₂ 2.33 X 10-3 V₂ 1.75

R₃ 746.44 I₃ 3.51 X 10-3 V₃ 2.62

R₄ 743.59 I₄ 1.17 X 10-3 V₄ 0.87

R₅ 743.59 I₅ 1.17 X 10-3 V₅ 0.87

Determining the Currents and Potential Differences for Resistors With a Single Voltage Source

Table 7.1: Experimental data of resistance, current and voltage in circuit with single voltage source


R₁ 750.00 I₁ 3.51 X 10-3 V₁ 2.63

R₂ 750.00 I₂ 2.33 X 10-3 V₂ 1.75

R₃ 750.00 I₃ 3.51 X 10-3 V₃ 2.63

R₄ 750.00 I₄ 1.17 X 10-3 V₄ 0.87

R₅ 750.00 I₅ 1.17 X 10-3 V₅ 0.87

Table 7.2: Theoretical data of resistance, current and voltage in circuit with single voltage source

Determining the Currents and Potential Differences for Resistors With Two Voltage Source


R₁ 728.74 I₁ 2.47 X 10 -3 V₁ 1.80

R₂ 742.36 I₂ 2.29 X 10 -3 V₂ 1.70

R₃ 750.00 I₃ 2.28 X 10 -3 V₃ 1.71

R₄ 750.00 I₄ 2.28 X 10 -3 V₄ 1.71

R₅ 657.89 I₅ 2.28 X 10 -3 V₅ 1.50


R₁ 750.00 I₁ 2.47 X 10 -3 V₁ 1.85

R₂ 750.00 I₂ 2.28 X 10 -3 V₂ 1.71

R₃ 750.00 I₃ 2.28 X 10 -3 V₃ 1.71

R₄ 750.00 I₄ 2.28 X 10 -3 V₄ 1.71

R₅ 750.00 I₅ 1.90 X 10 -3 V₅ 1.43

Table 7.3: Experimental data of resistance, current and voltage in circuit with two voltage source

Table 7.4: Theoretical data of resistance, current and voltage in circuit with two voltage source

PERCENTAGE DIFFERENCE

Current, I (mA) Voltage, V (V) Percentage Difference (%)

Iᴇ Iᴛ Vᴇ Vᴛ Current, I Voltage, V

2.47 X 10-3 2.47 X 10-3 1.80 1.85 0.00 2.74

2.29 X 10-3 2.28 X 10-3 1.70 1.71 0.44 0.58

2.28 X 10-3 2.28 X 10-3 1.71 1.71 0.00 0.00

2.28 X 10-3 2.28 X 10-3 1.71 1.71 0.00 0.00

2.28 X 10-3 1.90 X 10-3 1.50 1.43 18.2 4.78

Current, I (mA) Voltage, V (V) Percentage Difference (%)

Iᴇ Iᴛ Vᴇ Vᴛ Current, I Voltage, V

3.51 X 10-3 3.51 X 10-3 2.62 2.63 0.00 0.38

2.33 X 10-3 2.33 X 10-3 1.75 1.75 0.00 0.00

3.51 X 10-3 3.51 X 10-3 2.62 2.63 0.00 0.38

1.17 X 10-3 1.16 X 10-3 0.87 0.87 0.86 0.00

1.17 X 10-3 1.16 X 10-3 0.87 0.87 0.86 0.00

Table 7.5: Percentage difference for experiment and theoretical data and voltage in circuit with single voltage source

Table 7.6: Percentage difference for experiment and theoretical data and voltage in circuit with two voltage source

SOURCES OF ERROR AND SUGGESTION

Random Error• The resistors is not placed in the right lane on the

circuit board. We will get a wrong reading of current that we want to obtain. Hence , it will cause a difference in our experimental result compared to the theoretical result.

• To overcome this problem , we must set up the component of the circuit well according to figure given.

Systematic Error• The longer time taken to take the current reading

causing the short circuit to happen in the ammeter. It causes the ammeter to malfunction.

• To overcome this, the reading must be taken immediately

Random Error• The voltage reading is taken when the reading does

not show the fixed reading• To overcome , try to take the reading that appears

for long period of time. Repeat the experiment several time and take the average reading.

DISCUSSION• The objectives were achieved as we can determined the

values of currents and potential differences across each resistor in the circuit. So our results confirmed the Kirchhoff’s Rules theory.

• It is helpful to use two principles of Kirchhoff’s Rules which are the junction rule and the loop rule in order to calculate the values of current and potential difference.

• The percentage different between the theory and experimental values of current and voltage are very little, which is the less than 10% except for R5 which is 18.2%. However, the experiment is still considered a success.

• In the circuit of one source of voltage, there are three values of current which are I1 = I3 , I2 and I4 = I5.

• In the circuit of two sources of voltage, there are three values of current which are I1 , I2 = I3 = I4 and I5 .

CONCLUSION To conclude, the experiment is a success. To analyze a more complicated DC circuit, Kirchhoff’s

Rules are more suitable to be used in order to determine the current and voltage of the circuit.

Two principles of Kirchhoff’s Rules which are the Junction Rules stated that at any points, the sum of all currents entering the junction must be equal the sum of all currents leaving the junction. Loop Rules stated that the sum of potential difference across each circuit element in loop must be zero.

The potential difference between theory and experimental value of current and voltage are little which is less than 10% except R5 which is 18.2% in the two voltage sources.

REFERENCE

• Physics(2010), James S. Walker, Pearson Education, Malaysia

• Laboratory Workbook, Foundation Physics II

Documents

KIRCHHOFF’S RULES