Group # Date: Names: DC Circuits Introduction In this experiment you will examine how to make simple DC measurements that involve current, voltage, and resistance. The current I through a resistor R with a potential difference V across it is given by Ohm s law, I = V R, where the voltage is expressed in volts (V), the resistance in ohms (Ω), and the current in amperes (A). The power dissipated by the resistor often referred to as Joule heating is given by P = I 2 R = V 2 R. Any network of resistors connected across a potential difference has the same behaviour as a single equivalent resistor, with some equivalent resistance R eq. That is, the equivalent resistor draws the same current and dissipates the same power as the resistor network. There are several ways in which the equivalent resistance can be determined. We describe two of them here. First, it can be determined by measuring the potential difference V across the network and the total current I drawn by the network, and then calculating R = V/I. Second, the equivalent resistance can be calculated from the individual resistances in the network by successively replacing series and parallel combinations of resistors by their equivalent resistors. Resistances in series and in parallel add to the equivalent resistance as given below (and studied in class): R eq = R + R 2 + R 3 +... series, R eq = R + R 2 + R 3 +... parallel. Note: Two or more resistors form a series combination if the current that flows through one is exctly the same current that flows through each of the others in the combination. Two or more resistors form a parallel combination if their respective ends are at the same potential. It follows that the potential difference across a resistor is the same for all resistors in a parallel combination.
Preliminary Problem For the following questions assume that R = 00 Ω, R 2 = 50 Ω, and R 3 = 300 Ω. (a) Calculate the equivalent resistance when all three resistors are connected in series. R eq = (b) Calculate the equivalent resistance when all three resistors are connected in parallel. R eq = (c) Calculate the equivalent resistance, the potential difference across R 3, and the current flowing through R 2 for the combination below: R 2 R 5V + R 3 R eq = V 3 = I 2 = 2
PROCEDURE I. Resistance Measurements. Use the resistor colour code given below to determine the nominal resistance values as labeled on each of your three resistors. For instance, a resistor marked with yellow, blue, orange, silver and green has a resistance of R = 46000 Ω, a tolerance of 0%, and a 5% failure rate per 000 hours of operation. (Note that the 5th ring may not always be present.) Write down your results using the table provided below. Colour Value black 0 brown red 2 orange 3 yellow 4 green 5 blue 6 violet 7 gray 8 white 9 gold ±5% silver ±0% st ring 2nd ring 3rd ring 4th ring 5th ring st digit 2nd digit number of zeros following tolerance quality (% failure rate per 000 hrs) Your digital multimeter, as discussed before, can be used as a voltmeter, ammeter, or ohmmeter, depending on the FUNCTION switch setting. Set the multimeter to be used as an ohmmeter and measure the resistance of each of the three resistors and compare with the colour code values. Resistor Colour Code Resistance (Ω) Tolerance (%) Measured resistance (Ω) 2 3 Are the measured values within the given tolerances? Note that when measuring the resistance with the ohmmeter, the resistance should be removed from the circuit, without any current flowing through it. For ordinary resistors the polarity of the ohmmeter is irrelevant. 3
2. Connect your three resistors in series and measure the equivalent resistance. Calculate the expected value and compare with the measured value. R meas = R calc = 3. Connect your three resistors in parallel and measure the equivalent resistance. Calculate the expected value and compare with the measured value. R meas = R calc = II. Current and Voltage Measurements When using an ammeter or a voltmeter, make sure that they are connected as discussed in class and that the proper polarity is observed. Specifically, the ammeter must be connected in series with the part of the circuit for which the current is to be measured. For the voltmeter, the complementary rule holds: it must be connected in parallel with the part of the circuit for which the potential difference is to be measured. It is usually best to set the meter on a higher scale than you anticipate needing before making a measurement, in order to avoid overloading the meter. You can then reduce the scale to obtain a more sensitive reading, if necessary. Also, whenever possible, make use of the automatic scale determination as labeled by the AUTO button. II.A. Series Circuit.. Wire the three resistors in series and connect to the power supply. Measure the voltage across each resistor, and across the combination. Do the individual voltages add up to the expected total? V V 2 V 3 V tot 2. Turn the power supply off. Connect now the multimeter so it is ready to measure current, and have an instructor check your circuit before you turn the power back on. Measure the current (the same for all resistors). I = 3. Use your measurements to compute the resistance of the series combination. Compare with the ohmmeter measurement in part I.2. above. R = 4
II.B. Parallel Circuit.. Turn the power supply off. Connect the three resistors in parallel and connect to the power supply. Connect the multimeter so it is ready to measure the current through R. After an instructor has approved your circuit, turn the power on and measure the current through R. Repeat the procedure and measure the currents through R 2 and R 3, as well as the current through the entire circuit. Do the individual currents add up to the expected total? I I 2 I 3 I tot 2. Measure the voltage drop the same through all resistors. V = 3. Similarly, use your measurements to compute the resistance of the parallel combination, and compare with the ohmmeter measurement in part I.3. above. R = Time: h 00 min. 5