EENG-201 Experiment # 1 Series Circuit and Parallel Circuits I. Objectives Upon completion of this experiment, the student should be able to: 1. ead and use the resistor color code. 2. Use the digital multi-meter as an Ohmmeter and oltmeter. 3. Set and adjust a DC power supply 4. Become familiar with the use of a breadboard. 5. erify equations for computing equivalent resistance. 6. erify Kirchhoff s oltage Law (KL). 7. erify Kirchhoff s Current Law (KCL). II. Material and Equipment 1 - NYIT supplied Lab Kit 1 - Digital Multi-Meter (DMM) 1-6.8 Ω, 100 Ω, 220 Ω, 330 Ω, 470 Ω, 1 kω 1-2.2 k Ω 2.7 kω, 4.7 kω, 33 kω, 270 kω, 1MΩ 1-1 kω potentiometer, 10 kω potentiometer III. Theory Ohm s Law Ohm's Law, with dc circuitry, deals with the relationship between voltage and current in a resistor. This relationship states that: The potential difference (voltage),, across a resistance,, is proportional to the current, I, through it. That is: Equivalent esistances = I * (1-1) Figure 1.1: Two resistors in series According to Ohm's law, the equivalent resistance T between B and A is T = 1 + 2 (1-2)
For N resistors connected in series, the equivalent resistance is written as: N = = T i i 1 (1-3) Figure 1.2: Two resistors in parallel Consider two resistors connected in parallel, as shown above in Figure 1.2. 1 1 1 = + T 1 (1-4) 2 For N resistors connected in parallel, the equivalent resistance is written as: 1 N 1 = i = (1-5) 1i T Kirchhoff s oltage Law Kirchhoff's oltage Law states that the algebraic sum of all voltage rises and voltage drops around a closed loop (or path) must equal zero. Figure 1.3: Kirchoff s oltage Law using a single loop In this loop we have: or - S + 1 + 2 + 3 = 0 (1-6) 1 + 2 + 3 = S (1-7) In the above equation, negative signs are assigned to voltage rises and positive signs are assigned to voltage drops. In Figure 1.3, from Ohm s law one can write: 1 = I* 1 ; 2 = I * 2 ; 3 = I * 3 Substituting these expressions into (1-7), one obtains: ( 1 *I) + ( 2 *I) + ( 3 *I) = S (1-8) EENG-201 Page 2
Kirchhoff s Current Law Kirchhoff's Current Law states that the algebraic sum of all currents entering and all currents leaving a node (an electrical connection point) must equal zero. Note the top line showing all the currents is really a common point or node. Figure 1.4: Kirchoff s Current Law using a single node For this node: or -I S + I 1 + I 2 + I 3 = 0 (1-9) I 1 + I 2 + I 3 = I S (1-10) In equation 1-9 a negative sign is assigned to the entering current and a positive sign is assigned to each of the branch currents that are leaving the node. From Ohm s law we know that: I 1 = ; 1 I 2 = ; 2 I = 3 3 Substituting these expressions into (1-10), one obtains: 1 + 2 + 3 = I S (1-11) I. Preparation 1. Calculate I T, T, 1, 2, 3, and 4 in Figure 1.5, assuming S =12, 1 = 220 Ω, 2 = 330 Ω, 3 = 470 Ω, and 4 = 1 kω. As part of the solution redraw the circuit showing assigned voltage polarities and assigned current directions. Also show a computer simulation (PSPICE, Micro-cap, etc.). Prepare a table that will contain calculated and measured values (to be obtained in the lab). EENG-201 Page 3
2. Show that all the voltages found in Figure 1.5 satisfy KL? Figure 1.5: Series Circuit for calculations 3. Calculate I T, I 1, I 2, I 3, and T in Figure 1.6, assuming S = 12, 1 = 1 kω, 2 = 2.7 kω, 3 = 4.7 kω. As part of the solution redraw the circuit showing assigned voltage polarities and assigned current directions. Also show a computer simulation (PSPICE, Micro-cap, etc.). Prepare a table that will contain calculated and measured values (to be obtained in the lab). 4. Show that all the currents found in the Figure 1.6 satisfy KCL?. Procedure Part I: Breadboard Layout Figure 1.6: Parallel Circuit for calculations A solder-less breadboard is the most common type of prototyping circuit board. Prototyping a circuit is the process of creating a model suitable for complete evaluation of its design and performance. This requires the circuit to be designed, built and tested in the laboratory. Theoretical calculations and computer simulation are part of the design process. Once the circuit configuration is determined, the circuit is built on a prototyping board. There are two main types of prototyping circuit boards: Solder-less Breadboards Perfboard A circuit built on a breadboard requires neither soldering nor wire wrapping the connections. Examine the breadboard in your kit. This board will be used throughout the semester. The breadboard has two terminal strips, four bus strips, and three binding posts as shown in Figure 1.7. Each bus strip has two rows of contacts. Each row is a common point, or node. Bus strips must be used as power and ground. EENG-201 Page 4
Each terminal strip has 2 sets of 5 rows. Each column of 5 contacts is a common tie point. Build circuits on the terminal strips by inserting the leads of circuit components into the contact receptacles and making connections with 22 AWG (American Wire Gauge) wire. Larger gauge wire will damage the board. Use the red and black binding posts for power supply connections. Part II: esistance Color Code Figure 1.7: Typical Solder-less Breadboard Choose any of the resistors and examine it closely with your partner. Notice that there are four color bands. otate the resistor so that last band (the color may be gold or silver) is on your right side as shown below. Using Figures 1.8 and 1.9 associate the resistor s color code with a value in Table 1.1. For that row in the table, determine the maximum and minimum resistor values, based on the tolerance color code. Color 1st band 2nd band Multiplier Tolerance Black 0 0 1 Brown 1 1 10 ±1% ed 2 2 100 ±2% Orange 3 3 1k Yellow 4 4 10k Green 5 5 100k ±0.5% Blue 6 6 1M ±0.25% iolet 7 7 10M ±0.10% Grey 8 8 ±0.05% White 9 9 Gold 0.1 ±5% Silver 0.01 ±10% Figure 1.8: esistor Color Code EENG-201 Page 5
Figure 1.9: eading the Color Code Percentage tolerance is used to determine the range of resistance level. This is calculated by taking the tolerance band value and multiplying it by the nominal value. (5%)*(3 kω) =0.15 kω (1-12) The maximum value of the resistance is the sum of the tolerance value and the nominal value. Maximum alue = 3 kω + 0.15 kω = 3.15 kω (1-13) The minimum value of the resistance is the subtraction of the tolerance value and the nominal value. Minimum alue = 3 kω - 0.15 kω = 2.85 kω (1-14) esistor Color Bands Color Minimum alue Maximum alue 6.8 Ω 100 Ω 2.2 kω 33 kω 270 kω 1 MΩ Table 1.1 Associating a resistor s color code with a value and finding a range Part III: Using the Digital Multi-Meter as an Ohmmeter Fixed resistor To measure the resistance of a resistor, use a Digital Multi-Meter (DMM). Connect the resistor into the bread broad Connect the Black Probe to the COM terminal and ed Probe to the terminal marked with Ω. Set the meter to Ω. Connect the Black Probe to one end of the resistor now connect the ed Probe to the other end of the resistor. EENG-201 Page 6
Set the meter to Ω function. Now that the meter has given a reading, compare the difference between the measured resistance and the nominal resistance. The percentage difference is calculated by: Complete Table 1.2. no minal _ value measured _ value % Difference= *100 no minal _ value Nominal alue Ohmmeter eading % Difference 6.8 Ω 100 Ω 2.2 kω 33 kω 270 kω 1 MΩ Table 1.2 Comparing measured resistance with nominal value ariable resistor A potentiometer (pot or variable resistor) is a three terminal device that is used primarily to control potential voltage levels. Figure 1.10 Potentiometer schematic To determine the maximum value of a potentiometer measure its fixed resistance. This is done between the outer two leads (1 and 3). Turn the control knob as far as it will go in the clockwise direction and record your answer in the table below. Now turn the control arm in the counterclockwise direction as far as it will go and record your answer. Now turn the control arm to any position between the two extremes and record the resulting resistances. EENG-201 Page 7
Clockwise Counterclockwise Any Position Table 1.3: Total esistance of a potentiometer as shaft is turned To have a desired resistance value, connect the ed Probe of the ohmmeter to either of outer terminal leads on the potentiometer (1 or 3 in Figure 1.10). Now connect the Black Probe to the inner terminal also known as the wiper, 2 in Figure 1.10 Turn the control knob as far as it will go in the clockwise direction and record your answer in the table below. Now turn the control arm in the counterclockwise direction as far as it will go and record your answer. Now turn the control arm to any position between the two extremes and record the resulting resistances. Clockwise Counterclockwise Any Position Table 1.4: esistance between wiper arm and outer lead of a potentiometer as shaft is turned Part I: Using the Digital Multi-Meter for DC oltage Measurements A voltmeter is a device for measuring voltage. The voltmeter is placed in parallel with the circuit element whose voltage is to be measured. ecall that two elements are in parallel when they share the same pair of nodes and hence share the same voltage. Locate the voltage adjustment knob, current adjustment knob, and the power switch on the power supply. Before you turn on the power supply rotate both the current and voltage adjustment knobs to the left. Turn on the power supply. Note that both readings of current and voltage are at zero. Now rotate the current knob about half way. Now set the voltage adjustment knob for a reading of 0.5. Take the DMM and connect the Black Probe to the COM terminal on the meter and ed Probe to the terminal marked with "" on the meter. Set the meter to ---- function. The ed Probe is connected to the higher positive (+) voltage terminal of the power supply and the Black Probe to the negative (-) voltage terminal of the power supply. Set the power supply to the following voltages as stated in the table below and record your data. Power Supply oltage DMM oltage eading 0.5 2.0 5.0 15 20 Table 1.5: oltage measurements with a DMM. EENG-201 Page 8
Part : Using the Digital Multi-Meter for Making Current Measurements To measure the dc current in Figure 1.11, set the DMM selector switch to A--. Connect the Black Probe to the COM terminal of the DMM and the ed Probe to the DMM terminal marked 300mA. Figure 1.11: Circuit where current is to be measured Insert the meter as shown in Figure (1-12) and read the display. Figure 1.12: Circuit using DMM to measure current Note: If you attempt to read current "ACOSS" any component (as in reading voltage), you will damage the equipment, or cause a dangerous situation! If you re not sure on how to measure current, please call over either your instructor or the lab tech. Part I: Construction of Circuits 1. Measure and record the resistance values for Figure 1.5. 2. Construct the circuit shown in Figure 1.5. (Do not connect the source.) Measure T with the DMM. 3. Connect the source as shown in Figure 1.5. Measure and tabulate 1, 2, 3, 4, T and I T using the assigned polarities and directions from your preparation. 4. Set the resistance of the 10 kω potentiometer to the measured valued of T of Figure 1.5. Construct the circuit shown in Figure 1.13 below and find T and I T. Compare your answer with the results from the preparation and Figure 1.5. Are there any changes? EENG-201 Page 9
Figure1.13: Circuit with 10 kω potentiometer adjusted to T 5. Measure and record the resistance values for Figure 1.6. 6. Construct the circuit shown in Figure 1.6. (Do not connect the source.) Measure T with the DMM. 7. Connect the source as shown in Figure 1.6. Measure I 1, I 2, I 3, and I T using the assigned polarities and directions from your preparation. 8. Set the resistance of the10 kω potentiometer to the measured valued of T of Figure 1.6. Construct the circuit shown in Figure 1.13 above and find T and I T. Compare your answer with the results from the preparation and Figure 1.6. Are there any changes? II. Questions 1. A resistor has a color code of : a. ed, Black, Orange, Gold b. What is the nominal value of its resistance? c. What is the tolerance? d. What is the expected range of resistance values? 2. When you measured the resistance in Table 1.2, did the value fall within the expected ranges determined by the tolerance. 3. Explain the results in Table 1.3 and Table 1.4. 4. How is a voltmeter connected to measure an unknown voltage? 5. Calculate the percentage differences between the values obtained in the preparation and the actual measured values. 6. Compare experimental and calculated values. 7. Demonstrate the satisfaction of KL and KCL. 8. When using a DMM to do a current measurement, the implicit assumption is that the meter resistance is 0. What will be the effect on the measurement if the resistance of the meter is not 0. EENG-201 Page 10