ECE 376 Laboratory

Experiment #0- Introduction to Laboratory Equipment and Electronic Concepts

Richard Chandra Chan

Lab Section 308

He Ren

02/16/2010

Objective

The main aim of this laboratory #0 is to get familiar and comfortable with the task of

operating the lab equipments such as the digital multimeter, the digital oscilloscope, and the

function generator. Furthermore, it also teaches one to assemble a circuit on a protoboard.

In addition, the lab helps to reinforce and confirm the validity of the theory learnt during

lecture such as the Kirchhoff’s current law (KCL), the Kirchhoff’s voltage law (KVL) and

the Ohm’s law.

Equipments

1. Digital Multimeter

2. Hewlett-Packard (HP) function generator

3. Digital Oscilloscope

4. Protoboard

5. Six resistors with a nominal value of 1 kΩ, 2.2 kΩ, 3.3 kΩ, 4.7 kΩ, 6.8 kΩ and 10 kΩ

Background

This laboratory section requires one to apply the concepts learnt during lecture.

Ohm’s law states that the voltage across conducting materials is directly proportional to the

current flowing through the material, or

v=Ri

where the constant of proportionality R is called the resistance.

Resistors have resistance and resistance between two points simply refers to the resistance to

the flow of current between those two points for a given voltage between them.

RAB=resistance=voltsampere

=ohms=Ω

It is often possible to replace relatively complicated resistor combinations with a single

equivalent resistor. For instance: Resistors can be arranged in series or parallel.

Resistors in series are additive:

Rt=R1+R2+R3

Resistors in parallel combine using the following:

Rt=1

(1R1

+1R2

+1R3

+1R4

+1R5

)

Kirchhoff’s Voltage and Current Laws (KVL and KCL) help to provide a technique for

predicting the theoretical value of voltage and current.

According to KVL, the sum of voltages in a closed loop is zero. In the above diagram, the

three possible paths in the circuit are:

1. 10=V1+V2

2. 10=V1+V3

3. 10=V1+V4

According to KCL, the sum of currents entering a node (or junction between two or more

circuit elements) is zero:

IR1=I R2+ I R3+ IR4

Data and Results

Table 1

Nominal Resistance (color code) in kΩ

Actual Resistance (measured) in kΩ

1 0.9952.2 2.143.3 3.284.7 4.706.8 6.8110 9.90

In the Table 1 above, the actual resistances of the resistors were measured using the

ohmmeter mode of the digital multimeter (DMM).

Table 2

circuitTheoretical (using nominal

values) in kΩTheoretical (using actual

values) in kΩMeasured in

kΩ

1 11.1 11.085 11.0812 0.6896 0.6865 0.6853 0.6896 0.6865 0.6854 10 9.9 9.895 ∞ ∞ ∞

The above Table 2 represents the equivalent resistance of the six circuits presented in the lab

manual from Figure 1. The theoretical equivalent resistances were calculated using the

nominal and actual values of the resistors. They were calculated using the method presented

in the background section (See Calculation at the back). Then, the measured resistances were

obtained using the ohmmeter mode of the DMM.

From Table 2, Circuit 2 and Circuit 3 have the same equivalent resistance values for the

theoretical and the measured. It is mainly due to the fact that they both have their resistors

arranged in a parallel manner, the only thing that is different is the way the parallel

arrangement is oriented (Figure 1 in lab manual). Circuit 5 is an open circuit, thus the resistor

would have an infinite resistance and there would not be any current.

Table 3

Nominal resistance (kΩ)

Measured Resistance (kΩ)

DC Voltage across (V)

AC Voltage across (V)

DC Current through (mA)

AC Current through (mA)

1 0.995 5.80 0 5.80 04.7 4.70 6.05 0 1.28 010 9.90 6.04 0 0.61 0

From Table 3 above, the value of the AC voltage and the AC current are both zero since only

a 6V DC is being supplied and so there would not be any fluctuation in the circuit for voltage

and current. This corresponds to the zero value for the AC voltage and AC current.

Table 4

Nominal resistance

in kΩ

Measured Resistance in

kΩ

DC Voltage

(DMM) in mV

AC Voltage (DMM) in V

DC Current (DMM) in μA

AC Current (DMM) in

mA

V peak to peak (oscilloscope) in V

1 0.995 2.50 4.02 2.513 4.04 12.06

4.7 4.70 2.50 4.18 0.532 0.89 12.06

10 9.90 2.50 4.21 0.253 0.43 12.06

The data presented in Table 4 is in a reverse position from that in Step 3 and now sinusoid

waveform with a 6 V amplitude at 1 kHz is being applied and thus the significant value will

be the AC voltage and current.

Table 5

Table 6

V1 (V) V2 (V) V3 (V) V4 (V)Theoretical 1.43 4.57 4.57 6.00Measured 1.42 4.56 4.56 5.97

Table 7

V*I (mW) V2/R (mW) I2R (mW) Sup. or Abs.R1 2.03 2.02 2.04 AbsR2 4.44 4.42 4.46 AbsR3 2.10 2.08 2.12 AbsVs 8.57 x x Sup

For the data analysis in Table 5, 6 and 7, we have selected the following values for the 3

resistors: R1= 1 kΩ, R2=4.7 kΩ and R3=10 kΩ. In Table 5 and 6 above, the theoretical

portion of the data was calculated using the nodal analysis method (See calculation at the

I1 (mA) I2 (mA) I3 (mA) I4 (mA)Theoretical 1.43 0.972 0.457 1.43Measured 1.43 0.974 0.460 1.43

back). Table 7 shows that the 3 resistors in Figure 3 of the lab manual absorb power while the

voltage source supplies the power. The slight difference between the values of the resistors in

the three columns of Table 7 might be attributed to the significant figures involved.

Otherwise, the three methods provide three equivalent ways of deriving power.

Post-Lab questions

Question 1

circuitTheoretical

(using nominal values) in kΩ

Theoretical (using actual values) in kΩ

Measured in kΩ

error relative to the measured values

using nominal values using actual values1 11.1 11.085 11.081 0.17% 0.04%2 0.6896 0.6865 0.685 0.67% 0.22%3 0.6896 0.6865 0.685 0.67% 0.22%4 10 9.9 9.89 1.11% 0.10%5 ∞ ∞ ∞ 0.00% 0.00%

From the above, the percentage errors between the theoretical and measured values are

basically small. Thus, the theoretical theory correctly predicts the calculation of the

equivalent resistance of the 6 circuits found in Figure 1.

Question 2

Ohm’s law was obeyed in Step 3. (See Calculations at the back)

Question 3

Supplying 100 volts DC across the 1 kΩ resistor would generate a power value of 10 W (See

calculation at the back). This will exceed the power rating of the resistor which will cause it

to overheat and burn. Moreover, applying a 100 volt supply is not safe.

Question 4

There was a difference between the DC and the AC measurements on the DMM for Step 3

and 4. This was because a DC voltage supply was used in step 3 while an AC voltage supply

was used in Step 4. The voltage supply in Step3 is independent of time while that in Step 4 is

dependent on time. This explains the significant results of the DC voltage and current in step

3 and also the significant results of the AC voltage and current in step 4.

In step 3, the AC voltage and current are both 0 V and 0 A respectively. On the other hand,

the DC voltage and current in step 4 are observed to be small in values. One plausible

explanation for those values might be due to the electrical noise in the digital multimeter.

Question 5

The peak-to-peak voltage measured on the oscilloscope in step 4 is basically twice the

amplitude of the voltage (2 V0) while the AC voltage on the DMM has a time component to it

and besides the voltage is calculated from this equation:

V=V 0sin (ωt )

Thus, this might explain for the difference in the two values.

Question 6

The current and voltage measurements of step 5 satisfy KCL and KVL (See calculation at the

back).

Question 7

See Calculation at the back

Question 8

See calculation at the back

Question 9

Power was conserved in the circuit of Figure 3.

Reason: All the resistors present in Figure 3 of the lab manual absorb power while the voltage

source is the only one that generates power. From the calculations done at the back and also

referring to Table 7, it can be seen that the power generated by the voltage source is

equivalent to the total power absorbed by the three resistors. Thus, we can conclude that

power is conserved.

Conclusion

The main conclusion that I can derive from this lab is that the Kirchhoff’s current law (KCL)

and the Kirchhoff’s voltage law (KVL) are satisfied as shown by the current and voltage

measurement using the DMM for a circuit in a closed loop.

In addition, power is also conserved for a circuit in a closed loop.