To verify Ohm's law, to study the voltage, current, and resistance relationships for circuits containing resistors in series and in parallel.
The voltmeter-ammeter method of the measurement of resistance.
Variable DC voltage supply, resistor board, connecting wires, and computer with current/voltage probes.
Electrical current is the amount of charge passing by a given point in a conducting path (circuit) per unit time:
The relationship between the voltage, current, and resistance in a metallic conductor is given by Ohm's law. It states as follows: If the temperature and other physical conditions of a metallic conductor are unchanged, the ratio of the potential difference across the conductor (V) to the current (I) is a constant. This constant ratio (R) is the resistance of the conductor.
The resistance of a metallic conductor depends only on its length, the area of cross-section, the material of the conductor and its temperature. It does not depend on either V or I. Ohm's law may be applied either to the entire circuit or to any portion of the circuit in which there is no emf (source of voltage). Whenever this law is applied to the entire circuit, the voltage to be used is the net emf E and the resistance is the total resistance Rt of the circuit
Fig. 1 Measurement of voltage battery by volt-meter
Because most ammeters have a very small resistance, they do not greatly affect the current. In Fig. 2 an ammeter A is shown in series with a resistor R in a simple circuit.
Fig. 2 Ammeter measuring of current in resistor
A straightforward technique for measuring the resistance of a resistor would be to measure V and I with a voltmeter and ammeter and find the ratio (Eq. 1). However, the introduction of meters into the circuit alters the circuit so that the measured values may not be the same as the actual values. Figures 3 and 4 show two methods of connecting a voltmeter and ammeter to determine the resistance R.
In the first method (Fig. 3) the ammeter A measures the total current I in the main circuit, but a portion of this current, Iv, shunted around R through the voltmeter. Hence, the ammeter reading does not give the exact value of the current I' in R, and, consequently, V/I does not give the exact value of R. The voltmeter reads the potential difference V between its own terminals as well as across the resistance R, so that here the voltmeter reading (V) is equal to V'.
If the resistance of the voltmeter Rv is known, the value of Iv is given by
The second method of connecting the meters is shown in Fig 4.
In this arrangement, the ammeter reads the correct value of the current
I' passing through the resistor, but the voltmeter V reads the potential
drop across both the resistor R and the ammeter A. If Ra is
the resistance of the ammeter, then
If we have a complicated circuit including resistors in series and in parallel the best way to analyze it is to break it down into equivalent simple resistances.
Resistors in Series. Conductors are said to be connected in series when they are joined as shown in Fig 5 so that electricity flows uniformly from one resistor into the next.
Fig. 5 Resistors in series
In this case:
1. The current in all of the resistors in a series circuit is the same
Fig. 6 Resistors in parallel
In this case:
1. The currents in the various resistors are different and are inversely proportional to the respective resistances. The total current is the sum of the individual currents.
Set up Procedure:
1. Make sure all power supplies are OFF, and that the voltage meter range is set to 10 V, and the voltage adjust knob is zeroed. Set the Short Circuit Current to 225 mA.
2. Plug in the Dual Channel Amplifier wires. Din 1 goes to Din 1 on the ULI box, and Din 2 goes to Din 2. Take a current box and plug it into Probe 2 on the Dual Channel Amplifier (this serves as the Ammeter in the circuits.) Plug the voltage probe (with the alligator clips) into Probe 1 on the Dual Channel Amplifier. This is your voltmeter.
3. Double click on the Logger Pro folder, open the UTC Physics
folder, then open "Ohm's Law PT.MBL". Click on the "zero"
button at the top of the screen to zero all sensors. Click on the "Collect"
icon and erase the most recent data and graph. In taking the following
data, be careful to keep the voltage less than 5.0 V.
1. Connect the desired circuit shown in Figure 3. If you are using a resistor board with an even number on it, use resistor B. If you are using an odd-numbered resistor board, use resistor E.
2. Click on the Start button. Turn on the voltage supply. Set the voltage reading on the power supply to 0. Gradually increase the voltage and press the "KEEP" button. Repeat this procedure until you have collected 8 points, making sure that you keep the voltage level beneath 5 V.
3. Now, click on Stop.
4. Go to Analyze and drag to Automatic Fitů A window appears.
8. Connect the circuit for three resistors in series shown in Figure 5. Use the same three resistors. Repeat the Data Collection Procedure. Print the obtained graph.
9. Connect the circuit for three resistors in parallel shown in Figure 6. Use the same three resistors. Repeat the Data Collection Procedure. Print the obtained graph.
10. Close the Logger Pro program (do not save anything). Shut down the computer by clicking on Start icon at the bottom left-hand corner of the screen, and choose "shut down".
11. Disconnect all circuits and leave the materials as they were on the lab bench.
1. The slopes of the graphs obtained are the respective resistances for each circuit as can be seen in equation (1). Report the resistances in your results and conclusions as R ±DR W.
2. Using the experimentally measured resistances for the three individual resistors, compute a theoretical value for the total resistance of the series circuit. Compare this with the experimentally obtained value of resistance for the series circuit. Compare the experimental and calculated values. Are they within the experimetal error?
3. Using the experimentally measured resistances for your three individual resistors, compute a theoretical value for the total resistance of the parallel circuit. Compare this with the experimentally obtained value of resistance for the parallel circuit. Compare the experimental and calculated values. Are they within the experimetal error?
You should know what was plotted on the graphs and how such a graph yields the resistance of the circuit. Include all of your original data in your lab report and show your calculations for the data analysis questions. In your results and conclusions, you should report the values of resistance obtained for each individual reistor. Also include the answers to data analysis questions 2 and 3.