PHYSICS 262 LAB: Ohm’s law.

PHYSICS 262 LAB: Ohm's law.

Introduction.

            Ohms law states that V=IR where V is the voltage across the resistor, I the current through the resistor and R the resistance value characteristic of the resistor. Resistors are circuit components used in electrical circuits to control the current and voltage as given by the Ohm's law. Resistors in a circuit can be arranged in either a series or parallel pattern. The equation of the power of currents flowing across a voltage difference for any device is given by P=IV. Substituting the Ohm's law in the equation gives

Objective.

            The lab investigates the currents and voltages in both parallel and series circuit arrangements.

Apparatus.

            Computer for excel, Adjustable AC/DC power supply with digital readouts, multimeter used as ammeter, multimeter used as voltmeter, 100 and 33 Ohms resistor for RLC board, the electrical wires and alligator clips.

Procedure A: Current and Voltage for a single resistor.

1.      With the power supply off, we connected a multimeter set to the 2A DC ammeter setting and 33 Ohm resistor on the RLC board in series, making sure the positive lead goes into the input on the multimeter and the lead between the ammeter and the meter and the resister out from the common input of the multimeter as shown below.

2.      Before turning on the power supply, we had the TA check the connection. It is important to make sure that the multimeter is connected in series with the power supply and the resistor to avoid damage to it or blow-up of the fuse.

3.      We turned off the voltage and current knobs before turning on the supply to prevent any current from flowing before finding the voltage and current limits for the circuit.

4.      Majority of the resistors only dissipate about one-half watt before they overheat and potentially damaged. Using equation 3-3, we calculated the maximum voltage for the 33 Ohm resistor given P=0.5 watts as follows.

5.      Started data collection by setting the voltage to a low value of -0.25 to 0.50V, then recording the corresponding current. The voltage was increased in steps of -0.5V until the voltage limited calculated above was reached. This gave 8 points for plotting on a V vs I graph.

6.      Plotted and saved the graph of V and I in excel and used regression tools in excel to get the slop of the line through the V-I data points. From Ohms law, the slope represented the resistance of the circuit.

Procedure B: Current and voltage for series resistors, Kirchoff's laws.

1.      Repeated procedures A using 100 and 33 ohms resistors in series. The peak voltage reached 6v and the corresponding current recorded. The graph was drawn, and the slope to represent the total resistance obtained.

2.      Fixed the power supply voltage at 5v. The voltage across the 100 Ohm and 33 Ohms resistors were measured separately and recorded. The corresponding ammeter readings were also recorded.

3.      The sum of the two voltages obtained and compared with the power supply voltage.

Procedure C: Current and voltage for parallel resistors.

1.      Procedure A was repeated but using the 100 and 33 ohms resistors arranged in parallel. The peak voltage was set at 4V. Values of the corresponding currents were obtained and a graph drawn to obtain the slope which represented the equivalent resistance of the circuit.

2.      Power supply voltage was fixed at 3V and voltages measured across the two resistors recorded. Corresponding currents were also recorded.

3.      The voltages found were used to calculate the currents in each resistor. The sum of currents in each resistor was compared with the current out of the power supply.

Results and Discussion.

Procedure A.

Table 1
Trials	V	I	R
1	0.3	0.011	27.27
2	0.7	0.021	33.33
3	1.1	0.035	31.43
4	1.5	0.047	31.91
5	1.9	0.057	33.33
6	2.3	0.07	32.86
7	2.7	0.083	32.53
8	3.1	0.094	32.98

 

Figure 1: A graph of V vs. I for the results obtained in procedure A

Procedure B.

Table 2
Trials	V	I	R
1	0.7	0.006	116.67
2	1.4	0.011	127.73
3	2.1	0.016	131.25
4	2.9	0.022	131.82
5	3.5	0.027	129.63
6	4.2	0.032	131.25
7	4.9	0.037	132.43
8	5.6	0.042	133.33

 

Figure 2: The graph of V vs. I for the results obtained in procedure B

 

 

Table 3
Trials	V	I	R
1	0.4	0.016	15
2	0.8	0.034	23.5
3	1.2	0.048	22
4	1.6	0.063	25.4
5	2	0.079	25.32
6	2.4	0.097	24.74
7	2.8	0.112	25
8	3.2	0.129	24.8

Figure 3: A graph of V vs. I for the results obtained in procedure C

Analysis Questions.

1.      Using the rules for adding series resistors, how well did the net resistance you measured for the series circuit compare to the theoretical value for the resistance of two 100 and 33 Ohm resistors in series.

.

From the slope of the graph in table 2 which represents the resistance, R=134.92 which is slightly more than the theoretical value.

2.      Using the rules for adding parallel resistors, how well did the net resistance you measured for the series circuit compare to the theoretical value for the resistance of two 100 and 33 Ohm resistors in series.

.  =24.81. However, the slope of the curve of table 3 give R= 24.983 which is slightly higher.

3.      How are your values for the voltages across each resistor when the power supply voltage was fixed relate to Kirchoff's voltage law and Kirchoff's current law for the series circuit?

In the series circuit, the same current flows though the resistors. The power supply voltage equals the sum of voltage drops across the two resistors.

4.      How are your values for the current across each resistor when the power supply voltage was fixed relate to Kirchoff's voltage law and Kirchoff's current law for the parallel circuit?

In the parallel circuit, different currents flow through the resistors. By applying the Kirchoff's current law and current divider rule, more current comparatively flows in the 33 resistor than the 100.  Moreover, applying the Kirchoff's voltage law, voltage drops across the resistors arranged in series is the same. Therefore, in the parallel circuit, the same power supply voltage flows through the circuit.

Conclusion.

In the experiment, the ohm's law was very important in determining the resistance across the series and parallel arrangement, voltage drops using Kirchoff's voltage law and currents flowing through the resistors. The rule of adding the resistances was compared with the results obtained for several trials and the results were close enough to prove the rule.