DC Electrical Circuiits Laboratory Manual

laboratory manual for dc electrical circuits
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DC Electrical Circuits DC Electrical Circuits Laboratory Manual Laboratory Manual J Ja am me es s M M.. F Fiio orre e1 The Electrical Laboratory Objective The laboratory emphasizes the practical, hands-on component of this course. It complements the theoretical material presented in lecture, and as such, is integral and indispensible to the mastery of the subject. There are several items of importance here including proper safety procedures, required tools, and laboratory reports. This exercise will finish with an examination of scientific and engineering notation, the standard form of representing and manipulating values. Lab Safety and Tools If proper procedures are followed, the electrical lab is a perfectly safe place in which to work. There are some basic rules: No food or drink is allowed in lab at any time. Liquids are of particular danger as they are ordinarily conductive. While the circuitry used in lab is normally of no shock hazard, some of the test equipment may have very high internal voltages that could be lethal (in excess of 10,000 volts). Spilling a bottle of water or soda onto such equipment could leave the experimenter in the receiving end of a severe shock. Similarly, items such as books and jackets should not be left on top of the test equipment as it could cause overheating. Each lab bench is self contained. All test equipment is arrayed along the top shelf. Beneath this shelf at the back of the work area is a power strip. All test equipment for this bench should be plugged into this strip. None of this equipment should be plugged into any other strip. This strip is controlled by a single circuit breaker which also controls the bench light. In the event of an emergency, all test equipment may be powered off through this one switch. Further, the benches are controlled by dedicated circuit breakers in the front of the lab. Next to this main power panel is an A/B/C class fire extinguisher suitable for electrical fires. Located at the rear of the lab is a safety kit. This contains bandages, cleaning swaps and the like for small cuts and the like. For serious injury, the Security Office will be contacted. A lab bench should always be left in a secure mode. This means that the power to each piece of test equipment should be turned off, the bench itself should be turned off, all AC and DC power and signal sources should be turned down to zero, and all other equipment and components properly stowed with lab stools pushed under the bench. 8 Laboratory Manual for DC Electrical Circuits It is important to come prepared to lab. This includes the class text, the lab exercise for that day, class notebook, calculator, and hand tools. The tools include an electronic breadboard, test leads, wirestrippers, and needlenose pliers or hemostats. A small pencil soldering iron may also be useful. A basic DMM (digital multimeter) rounds out the list. A typical breadboard or protoboard is shown below: This particular unit features two main wiring sections with a common strip section down the center. Boards can be larger or smaller than this and may or may not have the mounting plate as shown. The connections are spaced 0.1 inch apart which is the standard spacing for many semiconductor chips. These are clustered in groups of five common terminals to allow multiple connections. The exception is the common strip which may have dozens of connection points. These are called buses and are designed for power and ground connections. Interconnections are normally made using small diameter solid hookup wire, usually AWG 22 or 24. Larger gauges may damage the board while smaller gauges do not always make good connections and are easy to break. In the picture below, the color highlighted sections indicate common connection points. Note the long blue section which is a bus. This unit has four discrete buses available. When building circuits on a breadboard, it is important to keep the interconnecting wires short and the layout as neat as possible. This will aid both circuit functioning and ease of troubleshooting. Laboratory Manual for DC Electrical Circuits 9 Laboratory Reports Unless specified otherwise, all lab exercises require a non-formal laboratory report. Lab reports are individual endeavors not group work. The deadline for reports is one week after the exercise is performed. A letter grade is subtracted for the first half-week late and two letter grades are subtracted for the second half-week late. Reports are not acceptable beyond one week late. A basic report should include a statement of the Objective (i.e., those items under investigation), a Conclusion (what was found or verified), a Discussion (an explanation and analysis of the lab data which links the Objective to the Conclusion), Data Tables and Graphs, and finally, answers to any problems or questions posed in the exercise. Details of the structure of the report along with an example report may be found at http://www2.mvcc.edu/users/faculty/jfiore/reportformat.html Scientific and Engineering Notation Scientists and engineers often work with very large and very small numbers. The ordinary practice of using commas and leading zeroes proves to be very cumbersome in this situation. Scientific notation is more compact and less error prone method of representation. The number is split into two portions: a precision part (the mantissa) and a magnitude part (the exponent, being a power of ten). For example, the rd value 23,000 could be written as 23 times 10 to the 3 power (that is, times one thousand). The exponent may be thought of in terms of how places the decimal point is moved to the left. Spelling this out is awkward, so a shorthand method is used where “times 10 to the X power” is replaced by the letter E (which stands for exponent). Thus, 23,000 could be written as 23E3. The value 45,000,000,000 would be written as 45E9. Note that it would also be possible to write this number as 4.5E10 or even .45E11. The 10 Laboratory Manual for DC Electrical Circuits only difference between scientific notation and engineering notation is that for engineering notation the exponent is always a multiple of three. Thus, 45E9 is proper engineering notation but 4.5E10 isn’t. On most scientific calculators E is represented by either an “EE” or “EXP” button. The process of entering the value 45E9 would be depressing the keys 4 5 EE 9. For fractional values, the exponent is negative and may be thought of in terms how many places the decimal point must be moved to the right. Thus, .00067 may be written as .67E-3 or 6.7E-4 or even 670E-6. Note that only the first and last of these three are acceptable as engineering notation. Engineering notation goes one step further by using a set of prefixes to replace the multiples of three for the exponent. The prefixes are: E12 = Tera (T) E9 = Giga (G) E6 = Mega (M) E3 = kilo (k) E-3 = milli (m) E-6 = micro (µ) E-9 = nano (n) E-12 = pico (p) Thus, 23,000 volts could be written as 23E3 volts or simply 23 kilovolts. Besides being more compact, this notation is much simpler than the ordinary form when manipulating wide ranging values. When multiplying, simply multiply the precision portions and add the exponents. Similarly, when dividing, divide the precision portions and subtract the exponents. For example, 23,000 times .000003 may appear to be a complicated task. In engineering notation this is 23E3 times 3E-6. The result is 69E-3 (that is, .069). Given enough practice it will become second nature that kilo (E3) times micro (E-6) yields milli (E-3). This will facilitate lab estimates a great deal. Continuing, 42,000,000 divided by .002 is 42E6 divided by 2E-3, or 21E9 (the exponent is 6 minus a negative 3, or 9). When adding or subtracting, first make sure that the exponents are the same (scaling if required) and then add or subtract the precision portions. For example, 2E3 plus 5E3 is 7E3. By comparison, 2E3 plus 5E6 is the same as 2E3 plus 5000E3, or 5002E3 (or 5.002E6). Perform the following operations. Convert the following into scientific and engineering notation. 1. 1,500 2. 63,200,000 3. .0234 4. .000059 5. 170 Convert the following into normal longhand notation: 6. 1.23E3 7. 54.7E6 8. 2E-3 9. 27E-9 10. 4.39E7 Laboratory Manual for DC Electrical Circuits 11 2 DC Sources and Metering Objective The objective of this exercise is to become familiar with the operation and usage of basic DC electrical laboratory devices, namely DC power supplies and digital multimeters. Theory Overview The adjustable DC power supply is a mainstay of the electrical and electronics laboratory. It is indispensible in the prototyping of electronic circuits and extremely useful when examining the operation of DC systems. Of equal importance is the handheld digital multimeter or DMM. This device is designed to measure voltage, current, and resistance at a minimum, although some units may offer the ability to measure other parameters such as capacitance or transistor beta. Along with general familiarity of the operation of these devices, it is very important to keep in mind that no measurement device is perfect; their relative accuracy, precision, and resolution must be taken into account. Accuracy refers to how far a measurement is from that parameter’s true value. Precision refers to the repeatability of the measurement, that is, the sort of variance (if any) that occurs when a parameter is measured several times. For a measurement to be valid, it must be both accurate and repeatable. Related to these characteristics is resolution. Resolution refers to the smallest change in measurement that may be discerned. For digital measurement devices this is ultimately limited by the number of significant digits available to display. A typical DMM offers 3 ½ digits of resolution, the half-digit referring to a leading digit that is limited to zero or one. This is also known as a “2000 count display”, meaning that it can show a minimum of 0000 and a maximum of 1999. The decimal point is “floating” in that it could appear anywhere in the sequence. Thus, these 2000 counts could range from 0.000 volts up to 1.999 volts, or 00.00 volts to 19.99 volts, or 000.0 volts to 199.9 volts, and so forth. With this sort of limitation in mind, it is very important to set the DMM to the lowest range that won’t produce an overload in order to achieve the greatest accuracy. A typical accuracy specification would be 1% of full scale plus two counts. “Full scale” refers to the selected range. If the 2 volt range was selected (0.000 to 1.999 for a 3 ½ digit meter), 1% would be approximately 20 millivolts (0.02 volts). To this a further uncertainty of two counts (i.e., the finest digit) must be included. In this example, the finest digit is a millivolt (0.001 volts) so this adds another 2 millivolts for a total of 22 millivolts of potential inaccuracy. In other words, the value displayed by the meter could be as much as 22 millivolts higher or lower than the true value. For the 20 volt range the inaccuracy would be computed in like manner for a total of 220 millivolts. Obviously, if a signal in the vicinity of, say, 1.3 volts was to be measured, greater accuracy will be obtained on the 2 volt scale than on either the 20 or 200 volt scales. In contrast, the 200 millivolt scale would produce an overload situation and cannot be used. Overloads are often indicated by either a flashing display or a readout of “OL”. 14 Laboratory Manual for DC Electrical Circuits Equipment (1) Adjustable DC Power Supply model:________________ srn:__________________ (1) Digital Multimeter model:________________ srn:__________________ (1) Precision Digital Multimeter model:________________ srn:__________________ Procedure 1. Assume a general purpose 3 ½ digit DMM is being used. Its base accuracy is listed as 2% of full scale plus 5 counts. Compute the inaccuracy caused by the scale and count factors and determine the total. Record these values in Table 2.1. 2. Repeat step one for a precision 4 ½ digit DMM spec’d at .5% full scale plus 3 counts. Record results in Table 2.2. 3. Set the adjustable power supply to 2.2 volts via its display. Use both the Coarse and Fine controls to get as close to 2.2 volts as possible. Record the displayed voltage in the first column of Table 2.3. Using the general purpose DMM set to the DC voltage function, set the range to 20 volts full scale. Measure the voltage at the ouput jacks of the power supply. Be sure to connect the DMM and power supply red lead to red lead, and black lead to black lead. Record the voltage registered by the DMM in the middle column of Table 2.3. Reset the DMM to the 200 volt scale, re-measure the voltage, and record in the final column 4. Repeat step three for the remaining voltages of Table 2.3. 5. Using the precision DMM, repeat steps three and four, recording the results in Table 2.4. Data Tables Scale 2% FS 5 Counts Total 200 mV 20 V Table 2.1 Laboratory Manual for DC Electrical Circuits 15 Scale .5% FS 3 Counts Total 200 mV 2 V Table 2.2 Voltage Power Supply DMM 20V Scale DMM 200V Scale 2.2 5.0 9.65 15.0 Table 2.3 Voltage Power Supply DMM 20V Scale DMM 200V Scale 2.2 5.0 9.65 15.0 Table 2.4 Questions 1. For the general purpose DMM of Table 2.1, which contributes the larger share of inaccuracy; the full scale percentage or the count spec? 2. Bearing in mind that the power supply display is really just a very limited sort of digital volt meter, which voltages in Table 2.3 and 2.4 do you suspect to be the most accurately measured and why? 3. Assuming that the precision DMM used in Table 2.4 has a base accuracy spec of .1% plus 2 counts and is properly calibrated, what is the range of possible “true” voltages measured for 15.0 volts on the 20 volt scale? 16 Laboratory Manual for DC Electrical Circuits 3 Resistor Color Code Objective The objective of this exercise is to become familiar with the measurement of resistance values using a digital multimeter (DMM). A second objective is to learn the resistor color code. Theory Overview The resistor is perhaps the most fundamental of all electrical devices. Its fundamental attribute is the restriction of electrical current flow: The greater the resistance, the greater the restriction of current. Resistance is measured in Ohms. The measurement of resistance in unpowered circuits may be performed with a digital multimeter. Like all components, resistors cannot be manufactured to perfection. That is, there will always be some variance of the true value of the component when compared to its nameplate or nominal value. For precision resistors, typically 1% tolerance or better, the nominal value is usually printed directly on the component. Normally, general purpose components, i.e. those worse than 1%, usually use a color code to indicate their value. The resistor color code typically uses 4 color bands. The first two bands indicate the precision values (i.e. the mantissa) while the third band indicates the power of ten applied (i.e. the number of zeroes to add). The fourth band indicates the tolerance. It is possible to find resistors with five or six bands but they will not be examined in this exercise. Examples are shown below: 18 Laboratory Manual for DC Electrical Circuits It is important to note that the physical size of the resistor indicates its power dissipation rating, not its ohmic value. Each color in the code represents a numeral. It starts with black and finishes with white, going through the rainbow in between: 0 Black 1 Brown 2 Red 3 Orange 4 Yellow 5 Green 6 Blue 7 Violet 8 Gray 9 White For the fourth, or tolerance, band: 5% Gold 10% Silver 20% None For example, a resistor with the color code brown-red-orange-silver would correspond to 1 2 followed by 3 zeroes, or 12,000 Ohms (more conveniently, 12 k Ohms). It would have a tolerance of 10% of 12 k Ohms or 1200 Ohms. This means that the actual value of any particular resistor with this code could be anywhere between 12,000-1200=10,800, to 12,000+1200=13,200. That is, 10.8 k to 13.2 k Ohms. Note, the IEC standard replaces the decimal point with the engineering prefix, thus 1.2 k is alternately written 1k2. Similarly, a 470 k 5% resistor would have the color code yellow-violet-yellow-gold. To help remember the color code many mnemonics have been created using the first letter of the colors to create a sentence. One example is the picnic mnemonic Black Bears Robbed Our Yummy Goodies Beating Various Gray Wolves. Measurement of resistors with a DMM is a very straight forward process. Simply set the DMM to the resistance function and choose the first scale that is higher than the expected value. Clip the leads to the resistor and record the resulting value. Equipment (1) Digital Multimeter model:________________ srn:__________________ Procedure 1. Given the nominal values and tolerances in Table 3.1, determine and record the corresponding color code bands. 2. Given the color codes in Table 3.2, determine and record the nominal value, tolerance and the minimum and maximum acceptable values. 3. Obtain a resistor equal to the first value listed in Table 3.3. Determine the minimum and maximum acceptable values based on the nominal value and tolerance. Record these values in Table 3.3. Using the DMM, measured the actual value of the resistor and record it in Table 3.3. Determine the deviation percentage of this component and record it in Table 3.3. The deviation percentage may be found via: Deviation = 100 (measured-nominal)/nominal. Circle the deviation if the resistor is out of tolerance. 4. Repeat Step 3 for the remaining resistor in Table 3.3. Laboratory Manual for DC Electrical Circuits 19 Data Tables Band 4 Value Band 1 Band 2 Band 3 27 10% 56 10% 180 5% 390 10% 680 5% 1.5 k 20% 3.6 k 10% 7.5 k 5% 10 k 5% 47 k 10% 820 k 10% 2.2 M 20 % Table 3.1 20 Laboratory Manual for DC Electrical Circuits 4 Ohm’s Law Objective This exercise examines Ohm’s law, one of the fundamental laws governing electrical circuits. It states that voltage is equal to the product of current times resistance. Theory Overview Ohm’s law is commonly written as V = I R. That is, for a given current, an increase in resistance will result in a greater voltage. Alternately, for a given voltage, an increase in resistance will produce a decrease in current. As this is a first order linear equation, plotting current versus voltage for a fixed resistance will yield a straight line. The slope of this line is the conductance, and conductance is the reciprocal of resistance. Therefore, for a high resistance, the plot line will appear closer to the horizontal while a lower resistance will produce a more vertical plot line. Equipment (1) Adjustable DC Power Supply model:________________ srn:__________________ (1) Digital Multimeter model:________________ srn:__________________ (1) 1 kΩ resistor __________________ (1) 6.8 kΩ resistor __________________ (1) 33 kΩ resistor __________________ Schematic Figure 4.1 24 Laboratory Manual for DC Electrical Circuits Procedure 1. Build the circuit of Figure 4.1 using the 1 kΩ resistor. Set the DMM to measure DC current and insert it in-line between the source and resistor. Set the source for zero volts. Measure and record the current in Table 4.1. Note that the theoretical current is 0 and any measured value other than 0 would produce an undefined percent deviation. 2. Setting E at 2 volts, determine the theoretical current based on Ohm’s law and record this in Table 4.1. Measure the actual current, determine the deviation, and record these in Table 4.1. Note that Deviation = 100 (measured – theory) / theory. 3. Repeat step 2 for the remaining source voltages in Table 4.1. 4. Remove the 1 kΩ and replace it with the 6.8 kΩ. Repeat steps 1 through 3 using Table 4.2. 5. Remove the 6.8 kΩ and replace it with the 33 kΩ. Repeat steps 1 through 3 using Table 4.3. 6. Using the measured currents from Tables 4.1, 4.2, and 4.3, create a plot of current versus voltage. Plot all three curves on the same graph. Voltage is the horizontal axis and current is the vertical axis. Data Tables E (volts) I theory I measured Deviation 0 0 2 4 6 8 10 12 Table 4.1 (1 kΩ) Laboratory Manual for DC Electrical Circuits 25 E (volts) I theory I measured Deviation 0 0 2 4 6 8 10 12 Table 4.2 (6.8 kΩ) E (volts) I theory I measured Deviation 0 0 2 4 6 8 10 12 Table 4.3 (33 kΩ) Questions 1. Does Ohm’s Law appear to hold in this exercise? 2. Is there a linear relationship between current and voltage? 3. What is the relationship between the slope of the plot line and the circuit resistance? 26 Laboratory Manual for DC Electrical Circuits 5 Series DC Circuits Objective The focus of this exercise is an examination of basic series DC circuits with resistors. A key element is Kirchhoff’s Voltage Law which states that the sum of voltage rises around a loop must equal the sum of the voltage drops. The voltage divider rule will also be investigated. Theory Overview A series circuit is defined by a single loop in which all components are arranged in daisy-chain fashion. The current is the same at all points in the loop and may be found by dividing the total voltage source by the total resistance. The voltage drops across any resistor may then be found by multiplying that current by the resistor value. Consequently, the voltage drops in a series circuit are directly proportional to the resistance. An alternate technique to find the voltage is the voltage divider rule. This states that the voltage across any resistor (or combination of resistors) is equal to the total voltage source times the ratio of the resistance of interest to the total resistance. Equipment (1) Adjustable DC Power Supply model:________________ srn:__________________ (1) Digital Multimeter model:________________ srn:__________________ (1) 1 kΩ __________________ (1) 2.2 kΩ __________________ (1) 3.3 kΩ __________________ (1) 6.8 kΩ __________________ Schematics Figure 5.1 28 Laboratory Manual for DC Electrical Circuits Figure 5.2 Procedure 1. Using the circuit of Figure 5.1 with R1 = 1 k, R2 = 2.2 k, R3 = 3.3 k, and E = 10 volts, determine the theoretical current and record it in Table 5.1. Construct the circuit. Set the DMM to read DC current and insert it in the circuit at point A. Remember, ammeters go in-line and require the circuit to be opened for proper measurement. The red lead should be placed closer to the positive source terminal. Record this current in Table 5.1. Repeat the current measurements at points B and C. 2. Using the theoretical current found in Step 1, apply Ohm’s law to determine the expected voltage drops across R1, R2, and R3. Record these values in the Theory column of Table 5.2. 3. Set the DMM to measure DC voltage. Remember, unlike current, voltage is measured across components. Place the DMM probes across R1 and measure its voltage. Again, red lead should be placed closer to the positive source terminal. Record this value in Table 5.2. Repeat this process for the voltages across R2 and R3. Determine the percent deviation between theoretical and measured for each of the three resistor voltages and record these in the final column of Table 5.2. 4. Consider the circuit of Figure 5.2 with R1 = 1 k, R2 = 2.2 k, R3 = 3.3 k, R4 = 6.8 k and E = 20 volts. Using the voltage divider rule, determine the voltage drops across each of the four resistors and record the values in Table 5.3 under the Theory column. Note that the larger the resistor, the greater the voltage should be. Also determine the potentials V and V , again using the voltage divider rule. AC B 5. Construct the circuit of Figure 5.2 with R1 = 1 k, R2 = 2.2 k, R3 = 3.3 k, R4 = 6.8 k and E = 20 volts. Set the DMM to measure DC voltage. Place the DMM probes across R1 and measure its voltage. Record this value in Table 5.3. Also determine the deviation. Repeat this process for the remaining three resistors. Laboratory Manual for DC Electrical Circuits 29 6. To find V , place the red probe on point A and the black probe on point C. Similarly, to find V , AC B place the red probe on point B and the black probe on ground. Record these values in Table 5.3 with deviations. Data Tables I Theory I Point A I Point B I Point C Table 5.1 Voltage Theory Measured Deviation R1 R2 R3 Table 5.2 Voltage Theory Measured Deviation R1 R2 R3 R4 VAC V B Table 5.3 30 Laboratory Manual for DC Electrical Circuits Questions 1. For the circuit of Figure 5.1, what is the expected current measurement at point D? 2. For the circuit of Figure 5.2, what are the expected current and voltage measurements at point D? 3. In Figure 5.2, R4 is approximately twice the size of R3 and about three times the size of R2. Would the voltages exhibit the same ratios? Why/why not? What about the currents through the resistors? 4. If a fifth resistor of 10 kΩ was added below R4 in Figure 5.2, how would this alter V and V ? Show AC B work. 5. Is KVL satisfied in Tables 5.2 and 5.3? Laboratory Manual for DC Electrical Circuits 31 6 Parallel DC Circuits Objective The focus of this exercise is an examination of basic parallel DC circuits with resistors. A key element is Kirchhoff’s Current Law which states that the sum of currents entering a node must equal the sum of the currents exiting that node. The current divider rule will also be investigated. Theory Overview A parallel circuit is defined by the fact that all components share two common nodes. The voltage is the same across all components and will equal the applied source voltage. The total supplied current may be found by dividing the voltage source by the equivalent parallel resistance. It may also be found by summing the currents in all of the branches. The current through any resistor branch may be found by dividing the source voltage by the resistor value. Consequently, the currents in a parallel circuit are inversely proportional to the associated resistances. An alternate technique to find a particular current is the current divider rule. For a two resistor circuit this states that the current through one resistor is equal to the total current times the ratio of the other resistor to the total resistance. Equipment (1) Adjustable DC Power Supply model:________________ srn:__________________ (1) Digital Multimeter model:________________ srn:__________________ (1) 1 kΩ __________________ (1) 2.2 kΩ __________________ (1) 3.3 kΩ __________________ (1) 6.8 kΩ __________________ Schematics Figure 6.1 32 Laboratory Manual for DC Electrical Circuits Figure 6.2 Procedure 1. Using the circuit of Figure 6.1 with R1 = 1 k, R2 = 2.2 k and E = 8 volts, determine the theoretical voltages at points A, B, and C with respect to ground. Record these values in Table 6.1. Construct the circuit. Set the DMM to read DC voltage and apply it to the circuit from point A to ground. The red lead should be placed at point A and the black lead should be connected to ground. Record this voltage in Table 6.1. Repeat the measurements at points B and C. 2. Apply Ohm’s law to determine the expected currents through R1 and R2. Record these values in the Theory column of Table 6.2. Also determine and record the total current. 3. Set the DMM to measure DC current. Remember, current is measured at a single point and requires the meter to be inserted in-line. To measure the total supplied current place the DMM between points A and B. The red lead should be placed closer to the positive source terminal. Record this value in Table 6.2. Repeat this process for the currents through R1 and R2. Determine the percent deviation between theoretical and measured for each of the currents and record these in the final column of Table 6.2. 4. Crosscheck the theoretical results by computing the two resistor currents through the current divider rule. Record these in Table 6.3. 5. Consider the circuit of Figure 6.2 with R1 = 1 k, R2 = 2.2 k, R3 = 3.3 k, R4 = 6.8 k and E = 10 volts. Using the Ohm’s law, determine the currents through each of the four resistors and record the values in Table 6.4 under the Theory column. Note that the larger the resistor, the smaller the current should be. Also determine and record the total supplied current and the current IX. Note that this current should equal the sum of the currents through R3 and R4. 6. Construct the circuit of Figure 6.2 with R1 = 1 k, R2 = 2.2 k, R3 = 3.3 k, R4 = 6.8 k and E = 10 volts. Set the DMM to measure DC current. Place the DMM probes in-line with R1 and measure its current. Record this value in Table 6.4. Also determine the deviation. Repeat this process for the remaining three resistors. Also measure the total current supplied by the source by inserting the ammeter between points A and B. Laboratory Manual for DC Electrical Circuits 33