Kirchhoff's current law parallel circuit

DC Circuits Analysis

LABORATORY MANUAL

Lab # 3

Parallel Circuits and Kirchhoff’s Current Law

"Seek simplicity but distrust it."

--Alfred North Whitehead

Experiment : Parallel Circuits and Kirchhoff’s Current Law

Objective:

After performing this experiment, you will be able to:

1. Demonstrate that the total resistance in a parallel circuit decreases as resistors are added.

2. Compute and measure resistance and currents in parallel circuits

3. Apply Kirchhoff’s Current Law (KCL) to a parallel circuit.

4. Explain how to troubleshoot parallel circuits

Materials needed:

Resistors: 3.3 kΩ, 4.7kΩ, 6.8kΩ, 10kΩ one of each.

Multimeter (Ohmmeter)

Measurement Procedures:

1. Obtain the resistors listed in Table 3-1. Measure and record the value of each resistor.

Resistance Measurement – Comparison of Listed Value vs. Measured.

Resistor

Listed Value

Measured Value [Multimeter]

R1

3.3 kΩ

R2

4.7 kΩ

R3

6.8 kΩ

R4

10.0 kΩ

Table 3-1

2. In Table 3-2, you will tabulate the total resistance of several resistors connected in parallel. (Parallel connections are indicated with two parallel lines shown between the resistors.) Enter the measured value of R1 in the table. Then connect R2 in parallel with R1 and measure the total resistance as shown in Figure 3-1. Enter the measured resistance of R1 in parallel with R2 in Table 3-2.

image1.png

Figure 3-1

3. Add R3 in parallel with R1 ad R2. Measure the parallel resistance of all three resistors. Then add R4 in parallel with the other three resistors and repeat the measurement. Record your results in Table 3-2.

4. Complete the parallel circuit by adding the voltage source as shown in Figure 3-2. Measure the total current IT in the circuit and record it in Table 3-2.

Be certain that the ammeter is connected in series with the voltage source.

If you are not sure, have your instructor or TA check the circuit.

image2.png

Figure 3-2

5. Measure the voltage across each resistor, using the voltmeter. How does the voltage across each resistor compare to the source voltage?

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Measured Readings

R1

R1|| R2

R1|| R2|| R3

R1|| R2|| R3|| R4

RT (measured)

RT (Computed)

IT (measured)

Table 3-2

RT – Total Resistance [Effective value of R1, R1|| R2 - for each combination]

IT - Total current.

6. Use Ohm’s law to compute the branch current in each resistor. Use the source voltage and the measured resistances. Tabulate the computed currents in Table 3-3.

Calculated Values–Individual branch current in Resistors – by Ohms law.

I1 = VS/R1

I2 = VS/R2

I3 = VS/R3

I4 = VS/R4

I (computed)

Table 3-3

7. Use general current divider rule to compute the current in each branch.

Use the total current and total resistance that you recorded in Table 3-2.

Show your results in Table 3-4.

Compare the calculation using the current divider rule with the results using Ohm’s law.

Calculation of Branch Current – using Concept of Current Divider.

I1 = (RT/R1)∙IT

I2 = (RT/ R2) ∙ IT

I3 = (RT/ R3) ∙ IT

I4 = (RT/ R4) ∙ IT

I (computed)

Table 3-4

8. Demonstrate Kirchhoff’s current law for the circuit by showing that the total current is equal to the sum of the branch currents.

-------------------------------------------------------------------

9. Simulate a burned-out resistor by removing R4 from the circuit. What is the new

total current?

IT = -----------------------------

10. In step 9, you simulated an open resistor by removing it from the circuit, and you observed that the total current dropped. Explain how the open resistor could be found in this experiment from the observed change in current and the source voltage.

Write a conclusion in the space below: