DC Circuits - Kirchhoff’s Rules

Purpose: To study Kirchhoff’s rules as they apply to complex DC circuits.

Apparatus: Circuit board, 100 Σ resistor (R

1

), 10 Σ plug-in resistor (R

2

), 50 Σ plug-in

resistor (R

3

), 22 Σ resistor (R

4

), decade resistance box (variable R), switch, power

supply, digital multimeter.

References:

Fig. 6-1 (I) Switch closed (II) Switch open

R

1

= 100

Ω

R

3

= 50

Ω

R

2

= 10 Ω

Decade

Resistance

Box

Switch

Power

Supply

Discussion:

Kirchhoff’s rules provide a general procedure for analyzing dc circuits no

matter how complex they might be. The circuits of Fig. 6-1, (I) with the switch S closed

and (II) with the switch S open, will be used to test both the junction and loop rules,

which may be stated as follows:

1. The sum of the currents entering any junction in a circuit must equal the sum of

the currents leaving that junction.

2. The sum of the potential differences across all elements around any closed

circuit loop must be zero.

Procedure:

1. Measure each of the resistors, R

1

, R

2

, R

3

, R

4

, before connecting them in the

circuit. Use the digital multimeter set for the most sensitive ohms range. Each of the

resistances should be recorded to at least 3 significant figures.

2. Wire the circuit shown in figure 6-1 above, with the switch S in the closed

position. Ask your instructor to check the wiring before you begin to make

measurements.

3. Set the digital multimeter to measure voltages and set the range to 20V.

Measure the output voltage of the power supply (battery eliminator). It should be

approximately 5 volts.

4. Set the digital multimeter to the 2V range. Measure the voltage across R

1

,

adjusting the decade box so that the voltage across R

1

is as close to 2 volts as possible.

Record this voltage, keeping all significant figures.

5. Measure the magnitudes and directions (+ or -) of the voltage drops across each

of the resistors, including the decade resistance box. Record these measurements,

keeping all significant figures, in the data table provided on page 17.

6. Disconnect the decade resistance box from the circuit (one side is sufficient)

and measure its resistance as precisely as possible.

7. Open the switch S. Do not change the value of the decade resistance box.

Measure all voltages across the resistors as above and record these results in the table

provided.

Calculations:

1. Fill in the tables by calculating the current (to 3 significant figures) through

each of the resistors for each of the voltage measurements made above.

2. Carefully draw the circuit (I) corresponding to the case when the switch S is

closed. Show the direction of the current through each of the resistors. Identify and label

all of the junctions in this circuit. Identify each of the closed loops associated with this

circuit.

3. Based on your measurements, calculate the sum of the currents at each junction

and the sum of the voltages around each loop. You must keep track of the signs of all

currents and voltages.

4. Do the same calculations as above (steps 2 and 3) for the circuit corresponding

to the case when the switch S is open (II).

5. Solve the circuit, using Kirchhoff’s rules, for the case when the switch is open.

Use your measured values of the resistances and the measured value of the voltage source

to calculate the current through each of the resistors.

Questions to Be Answered in the Report:

1. Do your measurements agree, within experimental errors, with Kirchhoff’s

rules? Discuss your results.

2. For the circuit in which switch S is open, how do your measured values of the

currents compare with the calculated values? What might account for any

discrepancies?

3. If the voltage source had a significant internal resistance, would this affect the

results? Explain.

4. For each circuit (I and II), what is the total power dissipated in the resistors?

Show how you calculated this result.

5. For each circuit (I and II), which resistor dissipates the most power? Justify

your answer.

Data Tables:

Switch closed

R (ohms)

V (volts)

I (milliamps)

R

1

R

2

R

3

R

4

R

decade

Switch open

R (ohms)

V (volts)

I (milliamps)

R

1

R

2

R

3

R

4

R

decade

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