Experiment #3, Ohm s Law

Experiment #3, Ohm s Law 1 Purpose Physics 182 - Summer 2013 - Experiment #3 1 To investigate the -oltage, -, characteristics of a carbon resistor at room temperature and at liquid nitrogen temperature, a tungsten filament in an incandescent bulb and a semiconductor diode. 2 ntroduction An electrical circuit is any continuous path or array of paths along which current may flow. A circuit usually contains a battery or other sources of EMF to create the current. n addition, it may contain anything from a single wire to a complicated collection of wires, resistor, and other circuit elements. As for example, in a flashlight the path from one terminal of a flashlight battery through the lamp and back to the other terminal of the battery is a simple circuit. A string of Christmas tree lights plugged into a wall socket forms part of a circuit or it may be considered a circuit by itself. 2.1 -oltage (-) Characteristics of Circuit Elements: Ohm's Law Part A. f we apply an electric potential difference (age) across the ends of a long copper wire maintained at a constant temperature and measure the current that flows, we find that is proportional to and resistance R is a constant. The resistance is the same for all data points therefore independent on the direction (positive and negative) and magnitude of the current used. When versus is plotted, as shown in Figure 1, a straight line graph is obtained. Materials which obey this are referred to as ohmic conductors. This straight line is symmetric with respect to the origin: R(, ) = R(-, -). Note that if the current s magnitude is increased too much, the circuit element may start to heat up and loose its linear ohmic - characteristics. Ohm s law is given as = R. We define the resistance as R = / ohms. For an ohmic conductor, at a given temperature, R is a constant independent of and and is equal to the inverse of the linear slope of the versus graph for that conductor (Figure 1): R = That is, R = Part B. Tungsten is a metallic conductor, yet the - characteristics of a light bulb with a tungsten filament exhibit a nonlinear (Figure 2) behavior because the temperature of the filament varies from around 20 o C to around 3000 o C. The temperature increases as the power (P = in units of Watts) increases. The temperature of a hot filament can be accurately determined from

Physics 182 - Summer 2013 - Experiment #3 2 its electrical resistance. The resistance of the tungsten filament is not constant, but is dependent on the magnitudes of and. The light bulb has point symmetry which displays 180 degree rotational symmetry with respect to the origin. That is, the current-age curve is origin symmetric, i.e., the magnitude of the current flowing for a given applied age value is the same regardless of age polarity (positive or negative sign). The currents for 5 s and -5 s are approximately the same, however, the current changes direction (sign) when the age polarity changes. n Figure 2, resistance and power are approximately the same at each symmetric point, R(, ) = R(-, -), but changes at each symmetric point as both are dependent on and, the power. n terms of power, at each symmetric point, P(, ) = P(-, -). The magnitude of the power changes the temperature. The resistance in Figure 2 depends on the magnitude to the current and not its direction. Note that for tungsten, higher power means a higher temperature and a higher resistance. For the device in Figure 1, power is not significantly changing the temperature for the range of values of and used. Resistance for tungsten is: R = Part C. Many conductors are not ohmic devices. Figure 3 illustrates the - plot for a solid state diode. The plot is not symmetric and is not a straight line even though the temperature remains constant. The resistance for this device depends on the age and R is not a constant at a given temperature. As indicted by Figure 3, the current for this device is almost zero when the polarity of the age is reversed. Such devices are said to have asymmetric current-age characteristic curves corresponding to their asymmetric electrical structure. (A diode is a two terminal electronic device with an asymmetric current versus age curve). Here too, resistance is: R = t should be realized that the relationship = R, which is Ohm s law, is not by itself a statement that a device is ohmic. A conductor is said to be ohmic if is proportional to and R is a constant at a given temperature and is independent on the direction of the current. The relationship R = / remains as the definition of the resistance of a circuit element whether or not it is ohmic.

3 Experimental Apparatus and Procedure 3.1 Apparatus 1. DC power supply and connecting cables. Physics 182 - Summer 2013 - Experiment #3 3 2. Agilent 34405A digital -ohmmeter (to be used for age and resistance measurements). 3. Fluke 75 digital multi-meter (to be used for all current measurements). 4. Carbon resistor, six electric light bulb and a solid state diode. 3.2 Procedure. Measurements are entered into the data section of the Lab Report. Determination of the - characteristics of various electrical elements n the following studies, you will assemble the circuit shown in Figure 4 to measure the current through the circuit element as a function of the applied age across the element. The milliammeter (Fluke 75) must be connected in series with the circuit element, while the meter (Agilent 34405A) must be in parallel, i.e., across the ends of the circuit element. Make sure you associate a plus + (positive high potential) or minus - (negative low potential) sign to each age and current measurement. The correct range on the meter will determine the amount of digits after the decimal point. 3.2.1 Carbon Resistor Part A 1. 1. Measure the resistance of the 1kΩ resistor using the Agilent 34405A. The correct range on the meter will determine the amount of digits after the decimal point. Then assemble the circuit in Figure 4 using the 1kΩ carbon resistor at the end of the long wire. 1 kilo-ohm (kω) = 1000 ohms (Ω) 2. Set function and range switches on the digital meter (Agilent 34405A) to DC and 10 olts. The correct range on the meter will determine the amount of digits after the decimal point. Figure 4 3. Set the milliammeter (Fluke 75) function switch to. Make sure the meter is set to measure DC current. 4. Set the knob on the power supply to zero s (all the way counterclockwise) and plug in (if not already) the power supply and digital meter to 110 AC outlet. Turn on the digital meter and then have the TA instructor check out your circuit before turning on the electrical equipment. 5. Measure and record the current through the resistor as a function of the age across it

Physics 182 - Summer 2013 - Experiment #3 4 while increasing from 1 to 7 s in steps of 1. Before proceeding to the next step, set the power supply output back to zero s. 6. Reverse the direction of the applied age across the circuit element by reversing the leads on the power supply. Again measure and record the current through the resistor for applied ages across the resistor in 1 increments between -1 and -7 s (arbitrarily designated as the negative polarity of applied age). 7. Lower the power supply output to zero and reverse the leads on the power supply to return to the designated positive polarity of applied age. 3.2.2 Temperature dependence of resistance of carbon resistor. Part A 2. Place the 1kΩ carbon resistor in liquid nitrogen, and measure the resistance of the 1kΩ resistor using the Agilent 34405A. Repeat steps 5, 6 and 7 described above to obtain the current-age characteristic curve for the resistor in liquid nitrogen (T = -195.8 C). Carbon is a semimetal, and its resistance will increase when the temperature decreases. There is an energy gap between the valence and conduction bands and the probability of an electron going from valence to conduction is temperature dependent. 3.2.3 Six- Electric Light Bulb Part B. Disconnect the 1kΩ resistor from the circuit and connect a six- electric light bulb in its place (Figure 5). Measure the current-age characteristics between.5 to 5 s (plus and minus polarity) in 0.5 steps following the procedure above (steps 5, 6, and 7). Continue to read this section first before starting your measurements to see how the above steps will be modified. As you increase the age, the tungsten will increase in temperature. As the temperature does increase, first do.5 s, then -.5 s. Next will be -1 s followed by 1 s. Use this staggered method of increasing the for your light bulb measurements. Do not exceed 5 otherwise you will blow a fuse. Figure 5

3.2.4 Diode: Asymmetric Circuit Element Part C. Physics 182 - Summer 2013 - Experiment #3 5 The diode is said to be a "rectifying" circuit element since it conducts current in only one direction and for only one polarity of applied age. t can thus be used to produce direct current from alternating current. Disconnect the electric light bulb and assemble the circuit of Figure 6 using a diode as the element to be studied. Note that in Figure 6 that a 1kΩ resistor is placed in series with the diode to limit the current through the diode. Be careful. The meter is connected only across the diode. Measure the current-age relationship between 0.10 to 25.00 (see data table). Reverse the polarity on the power supply and measure the current-age relationship in the range 0 to -12 in steps of -3. 4 Calculations, Analysis and Graphs for Lab Report 4.1 Analysis of current-age data on ohmic and non-ohmic circuit elements 4.1.1 Graphical Analysis for Lab Report Plot three graphs, using the 18 x 25 cm graph paper, of the current (ordinate y axis) as a function of the age (abscissa x axis) for the current-age data obtained for each circuit element. The data for the 1 k resistor at room and liquid nitrogen temperatures (Parts 3.2.1 and 3.2.2) may be plotted together on the same graph. They are both straight line graphs with different slopes. You should do three graphs for this experiment: resistor, light bulb and diode. The graph of the diode should include positive data only for = 0.00 to 25.00. Use the total graph sheet for this positive data. Use the 25 x 18 cm graph paper for the three graphs in your submitted work. f a graph is not linear, just enter the data points as a curve is hard to draw. 4.1.2 Computations for Lab Report Figure 6 1. Use your vs. data and linear regression on your calculator to calculate the electrical resistance of the carbon 1kΩ resistor at room and liquid nitrogen temperatures. R = 1/(slope - graph). Use your graph to determine the linear data to enter into your calculator. Your linear regression calculations should include the coefficient of determination R 2. 2. Calculate the resistance when the age across the light bulb is both plus and minus.5 and 5 s. You should have four calculations. 3. Calculate the power when the age across the light bulb is both plus and minus.5 and 5 s. You should have four calculations. 4. Calculate the resistance of the diode when the current is at both 2.00 and 12.00.

Physics 182 - Summer 2013 - Experiment #3 6 5 Questions 1. Explain in a few sentences if the carbon resistor in 3.2.1 and 3.2.2 is an ohmic device. Explain why. 2. Does the resistance of the resistor in question 1 increase or decrease when it is cooled by liquid nitrogen? Why does this resistance change? 3. Compare your measured value of the resistance, R LN2, of the carbon resistor at liquid nitrogen temperature to the calculated resistance, R Cal, given by the following expression. This comparison should be given as a percent error. Use the calculated value below as the accepted value. R Cal = R Room [1 + a(t LN2 T Room )] a = -0.5 x 10-3 / o C (Negative temperature coefficient, as carbon is a semimetal.) R Room = Measured resistance at room temperature, T Room T LN2 and T Room from data sheet This expression approximates the temperature dependence of the resistance in the carbon resistor. Expect a large percentage when you do the percent error. This should be a positive number as the absolute value is used. % error = ( R LN2 R Cal / R Cal )*(100%) 4. a. Does the resistance of the electric light bulb depend on the direction of current flow through it? Explain. b. Does the resistance of the electric light bulb increase, decrease or remain constant as the power,, is increased? Consult your data table. c. Does the temperature of the light bulb filament increase, decrease or remain constant as the power,, to the bulb is increased? (Associate a higher with an increase in temperature.) 5. Does the diode conduct symmetrically when the current flows in the forward (positive age) and the reverse (negative age) direction? s the diode an ohmic device? Explain. 6 Conclusion This section should have a clear statement of the results of the experiment and the extent to which the results are in agreement with the theory being tested. When the experiment results in a measurement of a constant (e.g., the specific heat of aluminum at a given temperature) compare it with its established handbook value. Use percent error for this comparison. To make this comparison meaningful, you should include the impact of the experimental error on your results. This includes errors in plotting and reading linear graphs when determining their slope and intercept. n addition, please include a statement of what you have learned, a critique of the experiment, and any suggestions you have which you think could improve the experiment or the lab handout.

Physics 182 - Summer 2013 - Experiment #3 7 nstrumentation 1. The DC oltmeter measures the age difference between two points to which its terminals are connected. The meter is always connected in parallel to the part of the circuit across which the potential difference is to be measured (Figure A1). n this experiment the Agilent 34405A multi-meter is used to measure age differences and the resistance of the carbon resistor. 2. The DC Milliammeter measures the electric current between any two points to which its terminals are connected. To measure the current in any part of the circuit, the circuit must be broken at that point and the ammeter must be inserted in the gap with loose ends connected to its terminals, i.e., the meter is connected in series with that part of the circuit where the current is to be measured (Figure A2). The Fluke 75 battery powered multi-meter is used to measure the current in milliamperes in this experiment. 3. Connecting wire leads. Assumed to be made of a good conducting material, e.g., a metal such as copper, and of a large enough cross-section to have negligible resistance and age drop across them. 4. The DC Power supply is a device used to supply a constant source of EMF between its output terminals. The electric current flows internally in the power supply from the minus to the plus terminal. n the external circuit it flows from the plus to the minus terminal (Figure A3). The meter on the actual power supply is not accurate and should not be used to determine the output age. The Agilent 34405A multi-meter is used to measure ages.

Ohm's Law Data Sheet Physics 182 - Summer 2013 - Experiment #3 8 Data goes into the data section of the Lab Report. Keep it neat and organized. - Characteristics 3.2.1 and 3.2.2 Carbon Resistor at Room and Liquid Nitrogen Temperatures Room Temperature = T Room = o C Estimated error in reading thermometer. Error T = T = o C Liquid Nitrogen Temperature = T LN2 = -195.8 o C Table 1: Measurements of age and current from +1 to +7 and -1 to -7 in steps of 1 both at room temperature and at liquid nitrogen temperature. Be sure to enter + or - for both age and current. Room Temperature 3.2.1 Part A 1. R Room = kω at room temperature (Direct Measurement Using Agilent 34405A) oltage oltage 0.00 0.00 0.00 0.00

Physics 182 - Summer 2013 - Experiment #3 9 Liquid Nitrogen Temperature 3.2.2 Part A 2. R LN2 = kω at LN 2 temperature (Direct Measurement Using Agilent 34405A) oltage oltage 0.00 0.00 0.00 0.00 3.2.3 SX OLT LGHT BULB Part B. Measurements of age and current from +.5 to +5 and from -.5 to -5 in steps of ±0.5. oltage Resistance / ohms Power mw oltage Resistance / ohms Power mw 0.00 0.00-0.00 0.00 0.00-0.00 a. b. d. c. e. f. h. g. i. j. l. k. m. n. p. o. q. r. t. s.

3.2.4 DODE Part C. Physics 182 - Summer 2013 - Experiment #3 10 Measurements of age corresponding to the current from 0.10 to 25.00 and measurement of the current in the age range 0 to -12. oltage oltage 0.10 0.00 0.25-3.00 0.50-6.00 1.00-9.00 2.00-12.00 3.00 5.00 8.00 12.00 18.00 25.00