POLYTECHNIC UNIVERSITY Electrical Engineering Department EE SOPHOMORE LABORATORY Experiment 2 DC circuits and network theorems Modified for Physics 18, Brooklyn College I. Overview of Experiment In this experiment you will verify experimentally the basic properties of resistive circuits. Specifically, the major objectives are to a) Verify Kirchhoff s Current Law (also known as the junction rule and abbreviated here as KCL), Kirchhoff s Voltage Law (also known as the loop rule and abbreviated here as KVL), and Ohm's law. b) Experiment with the concepts of linearity and superposition. c) Verify Thevenin's theorem by measuring the v-i characteristics of a circuit at a pair of terminals. d) Demonstrate the theorem of maximum power transfer. II. Equipment Required 2 DC power supplies ( Range 0-20V ) 1 Digital Multimeter 1 Protoboard 1 4.7kΩ resistor 2 Ω resistors 2 Ω resistors 1 Decade resistance box III. Preparation for the Experiment (to be done together at the start of the lab session) a) With = 10V and = 1mA, analyze the circuit in Figure 2-1 and make a sketch of the circuit with all node potentials and currents labeled on the sketch. You should define the node potentials with respect to the reference node indicated. Verify by calculation 8
that KCL is satisfied at each node and that KVL is satisfied around each mesh in the circuit. a b 4.7k Figure 2-1 b) According to the linearity and superposition theorems, you should be able to express the voltage across terminals a-b as a linear combination of the independent sources, V ab = α + β. Calculate the proportionality constants α and β for the given circuit. c) Find the Thevenin equivalent circuit corresponding to terminals a-b in Fig. 2-1, if the current source is removed. d) What is the maximum power that can be drawn from terminals a-b in the circuit of part (c), and what load resistance will draw this maximum power? IV. Experimental Procedure a) On your protoboard, wire the circuit in Figure 2-2, leaving the two DC power supplies, and V b, turned off for the time being. Measure each of the resistor values with your multimeter before you place them on the board, and make a sketch of figure 2-2 to record the measured values (You will need to save this sketch for reference when you write the report for this lab). In figure 2-2, the circuitry enclosed in the dashed rectangle on the right will represent the ideal current source, in figure 2-1. You can adjust the value of by adjusting the voltage V b, and the Ω resistor in the dashed box will allow you to measure the current. 9
a b 4.7k V I V b Figure 2-2 Adjust the two DC power supplies so that = 10V and = 1mA. The best procedure is to use your digital multimeter to first adjust the power supply to obtain = 10V and then adjust the V b supply to obtain = 1mA. Next, using the multimeter, measure the volt drop across each of the four resistors outside the dashed box, and record the results on the sketch you have drawn, being sure to mark the proper polarities. Also measure V I, and record its value on your sketch. b) By adjusting the voltages of the two DC power supplies, you will now fill in the table below. First, set to 5V, then adjust the V b supply so that takes the values 0.2mA, 0.5mA, and 1.0mA successively, to fill in the first column of the table. Each time you adjust, measure the value of V ab and enter the number in the table box corresponding to the settings of and. Next, set to 10V and repeat the three adjustments to fill in the second column of the table. Finally, set to15v, and complete the table. 5V 10V 15V 0.2mA 0.5mA 1.0mA 10
c) Remove from your circuit the power supply and the Ω resistor contained in the dashed box on the right side of figure 2-2, and connect a load resistance (your decade box adjusted to maximum resistance) across terminals a-b (Remember to turn off all power supplies before making any changes in the circuit). The circuit should now look like figure 2-3. a R L b 4.7k Figure 2-3 Reset the power supply to 10V. Next, fill in the table below with 7 entry pairs by setting the load resistance successively to the values R L =, Ω, 5kΩ, Ω, 1kΩ, 500 Ω, 100Ω. For each new load setting measure the precise value of the load resistance and the value of V ab using your digital multimeter, and record them in the table below. R L V ab d) Now you will determine experimentally the load resistance that draws maximum power when connected across terminals a-b in the circuit of figure 2-3. For any given value of R L, the power delivered to R L is easily found by calculating P L = V ab 2 / R L. To determine the maximum power and the corresponding load resistance therefore, adjust the decade box to its maximum setting and then reduce its resistance in steps, each time measuring V ab and calculating P L from the formula given above. As you do this, do not measure the value of R L each time, but use the value indicated on the decade box to calculate P L. When you reach the value of R L that draws maximum power, record the 11
value of P L and then measure the value of R L for this point only, making sure you disconnect the decade box from the circuit before measuring its resistance. The value of R L found here should be equal to the Thevenin resistance as seen from terminals a-b. Now, in order to make an alternate measurement of the Thevenin resistance seen from terminals a-b for the circuit of figure 2-3, remove the power supply and replace it with a short circuit. Also check that the decade box is no longer connected, and then measure the resistance across terminals a-b using your digital multimeter. Record the measured value of R th. V. Report a) We know that for the circuit in figure 2-1 we should have V ab = α + β. Therefore, if we are given two pairs of source values ( 1, Is 1 ) and (Vs 2, Is 2 ) and the corresponding output values V ab 1 and V ab 2, we should be able to find the values of α and β from the following pair of linear equations: 1 1 1 Vab = αvs + βis 2 2 2 Vab = αvs + βis From the data you recorded in part (b) of the experiment, substitute the numbers from the (, ) pairs (5V, 0.2mA) and (15V, 1.0mA) into the above equations and solve for α and β. Then fill in the rest of the table below by using the formula V ab = α + β with the values of α and β that you have just found. 5V 10V 15V 0.2mA 0.5mA 1.0mA Compare the numbers in this table to those you measured in part (b) of the experiment, and explain any discrepancies you find. 12
b) Copy the R L and V ab values from the table you filled in during part (c) of the experiment into the table below, and then complete this table by using Ohm's law to find the I ab values, where I ab is the current flowing from terminal a to terminal b through R L. R L V ab I ab Next, plot V ab as a function of I ab on a sheet of graph paper. This is the v-i characteristic for the circuit of figure 2-3 and should, in theory, look like the graph below. V ab V oc slope = - R th 0 c I ab Estimate the slope of your graph and calculate R th. How does this value compare with the measured value of R th that you found using the digital multimeter in part (c) of the experiment? How does it compare with the value of R th you get when you short out the voltage source in figure 2-3 and combine the resistors theoretically (As usual, use the measured values for the resistors instead of those given in the figure)? Also find the open circuit voltage from your graph and draw the Thevenin equivalent circuit. Calculate the maximum power that can be drawn from this circuit. c) Compare values of P max and R th that you measured in part (d) of the experiment to those found in part (b) above. Once again, explain discrepancies. 13