# Lab #6 Ohm s Law. Please type your lab report for Lab #6 and subsequent labs.

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2 Lab #6 Ohm's Law Page 2 of 4 Comment on Suggested Procedure You probably will want to use this 4-part procedure for each separate section of a lab exercise. Some labs will have multiple sections, others might have only one. List of equipment/parts needed for Ohm's Law Your instructor will describe the items listed below. (1) A circuit board on which various circuit components may be wired together. (2) A 25 k potentiometer. A potentiometer is a resistor with a sliding arm which may be moved from one end of the resistance to the other. Notice that it has 3 terminals. (3) A 1-35 volt DC power supply. (4) An assortment of patch cords, clip leads, and resistors. (5) An ammeter for measuring current. Do not exceed the current rating of the ammeter. (6) A digital multimeter (DMM), with which you can measure voltages from 0 to 750 volts AC or 1000 volts DC, and resistances from 0 to 20 megohms. 1. Resistor Color Code, Voltage, and the DMM Find 4 or 5 resistors with different values. Read the resistance values from the color code. Use the resistor color-code sheet, you don't need to memorize the colors. Use the DVM/DMM to measure the actual resistance for these resistors. Compare your measured values with the color code values. Were the measured resistances within the rated tolerance for each resistor? Use your digital multi-meter (DMM) to measure some DC voltages. Use the 1-35 VDC power supply and a battery. When using the DMM, always start on the highest scale and work down to avoid damage to the DMM. 2. Ohm's Law Graph and Power Calculations Set up the circuit on the right. Let R = 3.3 k. Choose the voltage of the power supply so that the power dissipated by the 3.3 k resistor does not exceed 1/2 watt. Remember that power = VI and that

3 Lab #6 Ohm's Law Page 3 of 4 power also is equal to I 2 R = V 2 /R for Ohmic resistors. Ohmic means that Ohm's law holds, ie., V = IR, the graph of V vs. I passes through (0,0). Measure the current I flowing through the resistor R for at least five different settings of the power supply voltage. Also measure V across the resistor for each setting. Graph V R vs. I for the resistor. Compare the value of R found from the slope of the graph with the color code value. How do these values of R compare to the value measured with the digital multimeter? (You must take R out of the circuit to measure its resistance with the DMM. Why?) Find out (somehow) how the DMM measures resistance. Explain in your lab report. Do not exceed the power rating of the resistors. (The small color coded resistors are good for about 1/2 watt at most.) Calculate P = VI for each voltage-current combination. Show V, I, and Power in a neat table with 3 columns. Use Excel for the V-I graph! 3. Resistors in Series, Parallel, and Series/Parallel Note: For parts (A) through (E) you should use sets of resistors whose largest and smallest values do not differ from each other by more than a factor of 4. (You should include the values of R 1, R 2, & R 3 in your data set) (A) Use the DMM to measure the actual R for each of the resistors. (B) Use your DMM to determine the resistance of 2 resistors in series. Compare your measured value of R with the value you can compute from your measured values of R 1 and R 2. Show how you computed the equivalent resistance, R. (C) Repeat part (B) using 3 resistors in series. (D) Repeat part (B) using 2 resistors in parallel. (E) Repeat part (B) using 3 resistors in parallel. (F) Repeat part (A) using the two simple

4 Lab #6 Ohm's Law Page 4 of 4 series/parallel circuits shown below. (1) (2) 4. A Voltage Divider using a Potentiometer Use Ohm's Law to solve for V out (R 1 ) (voltage measured across R 1 ) as a function of V in and R 1 in the circuit below. If you don t understand how the 25 k potentiometer works, try measuring R 1 + R 2 25 k, and then measure R 1 or R 2 as a function of the shaft position. You really do need to understand this device! Note: In order to measure R 1 with the DMM, you must disconnect the potentiometer from the power supply. Why? Connect the 25 k potentiometer to the power supply as in this diagram. Set the power supply for some reasonable value of V in such as 12 volts, and measure V out as a function of R 1. NOTE: This requires that you use your DMM to measure R 1 and R 2 for each setting of the potentiometer. R 2 = 25 k - R 1! Graph V out as a function of R 1. Show how the graph agrees both qualitatively and quantitatively with your formula for V out as a function of R 1, R 2 and V in. In other words, compare your theoretical equation to the trend line equation from Excel. The circuit is called a voltage divider. Why? Does it represent a practical method of getting low voltages from very high voltages? Why or why not? Answer this, don't ignore it. (Hint: Think about power being lost or wasted by R 1 or R 2.) The DMM has an input impedance (resistance) of 10 megohms, so it does not draw an appreciable amount of current from this circuit. What would happen if the input resistance of the volt meter were about 25 kilohms? How would this affect your measurement of V?

5 Rev. 10/18/06 DKD Page 1 of 5 Montgomery College Rockville Campus Department of Physics, Engineering & Geosciences Lab #6 Supplement: Resistors, Capacitors, Inductors and the Resistor Color Code Introduction In this series of experiments we shall first observe simple direct current (D. C.) circuits. Following this we will study the behavior of a variety of electric circuits in which the voltages and currents vary with time. In these studies the most important instrument is the cathoderay oscilloscope, incorporating a cathode-ray tube very similar to the device used to study electron motion. As we shall see, the oscilloscope is an extremely useful instrument for observing and measuring rapidly varying voltages and currents in electric circuits. The circuits to be considered in these experiments contain various combinations of resistors, capacitors, inductors, batteries, and sinusoidal or square-wave voltage generators. Below are short discussions of the characteristics of resistors (R), capacitors (C), inductors (L), batteries, and voltmeters (Digital Multi-Meters, DMM). (A) Resistors An ideal resistor has the property that when a potential difference V is applied between its terminals, the resulting current I is directly proportional to V and inversely proportional to the electrical resistance (R) of the resistor. That is, for an ideal resistor I = V/R or V = IR or R = V/I These algebraic relations are called Ohm's Law. Ideal resistors obey Ohm's Law and have a V-I characteristic as graphed below. The slope of the V-I line, V/ I is the value of the resistance. Note that the line is straight and passes through (0,0). In the MKS system of units, where V is measured in volts and I in amperes, the unit of resistance is the ohm, abbreviated. The units k (10 3 ) and M (10 6 ) are also commonly used. In addition to resistance every resistor has a power rating, which is the maximum power (VI) which may be dissipated in the resistor. Exceeding this power rating will change the resistance in a unpredictable manner or destroy the device completely.

6 Rev. 10/18/06 DKD Page 2 of 5 Lab #6 Supplement: Resistors, Capacitors, Inductors and the Resistor Color Code Resistors of the type used in these experiments are common in electronic circuitry and typically have power ratings of ½ or 1 W (watt) which is the maximum power that can be dissipated without overheating. These resistors are usually made of a carbon-clay mixture which is fired to form a hard ceramic material; the resistance can be controlled by varying the proportions of ingredients. Resistors are labeled according to the color code shown at the end of this handout. For example, a resistor whose resistance is 56, % would have green, blue, orange, silver bands (reading inward from the band nearest the end). Many devices such as light bulbs with tungsten filaments display non-linear (non-ohmic) characteristics. The graph of V vs. I is NOT necessarily a straight line and it may not pass through (0,0). So V IR, R may differ from point to point along the curve, R = V/ I and R is NOT equal to V/I as is true in the Ohmic or ideal resistor case. Below are some possible graphs for V-I characteristics for non-linear devices. (B) Capacitors A capacitor may be thought of as a charge-storing device. When a charge Q is added to one plate and a charge -Q to the other, the resulting potential difference V between the plates is proportional to Q: this proportionality is expressed by the relation Q = CV or C = Q/V where C is a constant characteristic of the device, called its capacitance. In MKS units Q is measured in coulombs, and the corresponding MKS unit of capacitance is the farad, abbreviated F. One farad is an extremely large unit of capacitance; the units F (10-6 F) and pf (10-12 F) are usually used. Capacitors are often made from a long, narrow sandwich of aluminum foil and Mylar film (an insulating plastic) rolled into a cylinder and encased in plastic. In addition to capacitance, capacitors are also rated according to maximum instantaneous voltage which may be applied. Exceeding this rating will lead to dielectric breakdown and perforation of the insulating material, causing a short circuit which renders the device useless. The Mylar insulation for a capacitor rated at 100 V, is about 10 (microns) thick.

7 Rev. 10/18/06 DKD Page 3 of 5 Lab #6 Supplement: Resistors, Capacitors, Inductors and the Resistor Color Code A very useful equation relating I, V, and C (the usual circuit variables) can be derived from Q = CV. Take the time derivative of both sides as shown below and note that dq/dt is I and thus: Q = CV dq/dt = CdV/dt = I or I = C dv/dt

8 Rev. 10/18/06 DKD Page 4 of 5 Lab #6 Supplement: Resistors, Capacitors, Inductors and the Resistor Color Code (C) Inductors An inductor is a coil of wire, which may or may not have a powdered iron or ferrite core. A changing current in the coil produces a changing magnetic flux through it; this in turn induces a voltage V between the terminals which is proportional to the rate of change of the current di/dt. This relationship is expressed by the equation V = L di/dt where L is a constant characteristic of the device called the inductance. The MKS unit of inductance is the henry, abbreviated H. The units mh (10-3 H) and H (10-6 H) are commonly used. Inductance is defined as the ratio of /I, where is the magnetic flux; L = /I so = LI. Take the time derivative of both sides of the equation, then d /dt = L di/dt but d /dt = V (Faraday's Law) so finally we find V = L di/dt as noted above. This equation, along with I = C dv/dt and V = IR form a set which are most useful for analyzing electronic circuits. (D) Batteries, voltmeter An idealized battery is a device which produces a potential difference between its terminals which is constant and independent of the current through the device. The most familiar batteries are made from the same kind of carbon zinc dry cells as are used in flashlights. Each such cell has a potential of about 1.5 V. Thus a 45 V battery has 30 cells in series. In real batteries, the potential is not completely independent of current, but the behavior can be represented as an idealized battery with constant potential, in series with a fixed resistance, called the internal resistance of the battery. The internal resistance of a dry cell is about 0.1 ohms when new, but increases with age and use. In addition to the circuit devices discussed above, two other instruments will be used, a voltmeter or digital multi-meter (DMM) and a signal generator. The voltmeter, as its name implies, measures the potential difference between two points in a circuit. It is important to understand that when a voltmeter is connected in a circuit, it becomes part of the circuit, and the current flowing through the voltmeter must be taken into consideration. The amount of current flowing through the voltmeter is determined by its internal resistance. Older voltmeters typically had an internal resistance of the order of 10 3 to 10 5 ohms. Newer digital voltmeters have a much higher internal resistance; 10 M is common.

9 Rev. 10/18/06 DKD Page 5 of 5 Lab #6 Supplement: Resistors, Capacitors, Inductors and the Resistor Color Code (E) Kirchoff s Laws The basic physical principles used in the analysis of circuits are Kirchoff s circuit laws. The voltage law, or loop law, states that the algebraic sum of the potential differences around any closed loop must be zero. The current law states that the algebraic sum of the currents at any junction must be zero. These two laws, together with the characteristics of the circuit devices described above, provide a complete theoretical basis for the analysis of circuit behavior. The laws may be written as follows: (F) Resistor Color Code Code Basic Values Color 1 st Digit 2 nd Digit Multiplier Value 1 st Color 2 nd Color Silver Brown Black Gold Brown Red Black Brown Green Brown Brown Gray Red Red Red Orange Red Violet Yellow Orange Orange Green Orange White Blue Yellow Violet Violet Green Blue Gray Blue Gray White Gray Red Some examples: (1) Red Orange Green = 23 x 10 5 (2) Red Green Red = 25 x 10 2 (3) Orange Yellow Yellow = 34 x 10 4

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